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Journal articles on the topic 'Spectral asymptotic'

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Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Laursen, K. B., and M. M. Neumann. "Asymptotic intertwining and spectral inclusions on Banach spaces." Czechoslovak Mathematical Journal 43, no. 3 (1993): 483–97. http://dx.doi.org/10.21136/cmj.1993.128413.

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2

Bunoiu, Renata, Giuseppe Cardone, and Sergey A. Nazarov. "Scalar problems in junctions of rods and a plate." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 2 (March 2018): 481–508. http://dx.doi.org/10.1051/m2an/2017047.

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In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the eigenvalues, we employ two equipollent asymptotic models posed on the skeleton of the junction, that is, a hybrid domain. We, first, use the technique of self-adjoint extensions and, second, we impose algebraic conditions at the junction points in order to compile a problem in a function space with detached asymptotics. The latter problem is involved into a symmetric generalized Green formula and, therefore, admits the variational formulation. In comparison with a primordial asymptotic procedure, these two models provide much better proximity of the spectra of the problems in the spacial junction and in its skeleton. However, they exhibit the negative spectrum of finite multiplicity and for these “parasitic” eigenvalues we derive asymptotic formulas to demonstrate that they do not belong to the service area of the developed asymptotic models.

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3

Lange, Ridgley. "Duality and asymptotic spectral decompositions." Pacific Journal of Mathematics 121, no. 1 (January 1, 1986): 93–108. http://dx.doi.org/10.2140/pjm.1986.121.93.

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4

Dahlhaus, Rainer. "Asymptotic normality of spectral estimates." Journal of Multivariate Analysis 16, no. 3 (June 1985): 412–31. http://dx.doi.org/10.1016/0047-259x(85)90028-4.

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5

Dubiner, Moshe. "Asymptotic analysis of spectral methods." Journal of Scientific Computing 2, no. 1 (March 1987): 3–31. http://dx.doi.org/10.1007/bf01061510.

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6

Dévoué, V., M. F. Hasler, and J. A. Marti. "Multidimensional asymptotic spectral analysis and applications." Applicable Analysis 90, no. 11 (February 23, 2011): 1729–46. http://dx.doi.org/10.1080/00036811.2010.524296.

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7

Taubes, Clifford Henry. "Asymptotic spectral flow for Dirac operators." Communications in Analysis and Geometry 15, no. 3 (2007): 569–87. http://dx.doi.org/10.4310/cag.2007.v15.n3.a5.

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8

Lii, K. S., and M. Rosenblatt. "Asymptotic normality of cumulant spectral estimates." Journal of Theoretical Probability 3, no. 2 (April 1990): 367–85. http://dx.doi.org/10.1007/bf01045168.

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9

Liu, Weidong, and Wei Biao Wu. "ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES." Econometric Theory 26, no. 4 (November 4, 2009): 1218–45. http://dx.doi.org/10.1017/s026646660999051x.

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We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

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10

Frank, Rupert L., and Simon Larson. "Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 766 (September 1, 2020): 195–228. http://dx.doi.org/10.1515/crelle-2019-0019.

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AbstractWe prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first two terms in the asymptotics.

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11

Kley, Tobias, Stanislav Volgushev, Holger Dette, and Marc Hallin. "Quantile spectral processes: Asymptotic analysis and inference." Bernoulli 22, no. 3 (August 2016): 1770–807. http://dx.doi.org/10.3150/15-bej711.

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12

Yi, Xinping. "Asymptotic Spectral Representation of Linear Convolutional Layers." IEEE Transactions on Signal Processing 70 (2022): 566–81. http://dx.doi.org/10.1109/tsp.2022.3140718.

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13

Kreisbeck, Carolin, and Luísa Mascarenhas. "Asymptotic spectral analysis in semiconductor nanowire heterostructures." Applicable Analysis 94, no. 6 (June 2, 2014): 1153–91. http://dx.doi.org/10.1080/00036811.2014.919052.

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14

Hora, Akihito, and Nobuaki Obata. "Asymptotic spectral analysis of growing regular graphs." Transactions of the American Mathematical Society 360, no. 02 (February 1, 2008): 899–924. http://dx.doi.org/10.1090/s0002-9947-07-04232-8.

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15

Allaire, Grégoire, and Carlos Conca. "Bloch wave homogenization and spectral asymptotic analysis." Journal de Mathématiques Pures et Appliquées 77, no. 2 (February 1998): 153–208. http://dx.doi.org/10.1016/s0021-7824(98)80068-8.

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16

Zhang, Chao, and Ben-yu Guo. "Generalized Hermite spectral method matching asymptotic behaviors." Journal of Computational and Applied Mathematics 255 (January 2014): 616–34. http://dx.doi.org/10.1016/j.cam.2013.06.018.

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17

Hillairet, Luc, and Chris Judge. "Spectral Simplicity and Asymptotic Separation of Variables." Communications in Mathematical Physics 302, no. 2 (January 15, 2011): 291–344. http://dx.doi.org/10.1007/s00220-010-1185-6.

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18

Räbiger, Frank, and Manfred P. H. Wolff. "Spectral and asymptotic properties of dominated operators." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 63, no. 1 (August 1997): 16–31. http://dx.doi.org/10.1017/s144678870000029x.

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AbstractWe investigate the relationship between the peripheral spectrum of a positive operator T on a Banach lattice E and the peripheral spectrum of the operators S dominated by T, that is, ]Sx] ≤ T]x] for all x ε E. This can be applied to obtain inheritance results for asymptotic properties of dominated operators.

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19

Shao, Xiaofeng, and Wei Biao Wu. "Asymptotic spectral theory for nonlinear time series." Annals of Statistics 35, no. 4 (August 2007): 1773–801. http://dx.doi.org/10.1214/009053606000001479.

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20

Volk, Kevin, and Sun Kwok. "Spectral evolution of asymptotic giant branch stars." Astrophysical Journal 331 (August 1988): 435. http://dx.doi.org/10.1086/166570.

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21

Gurarie, David. "Asymptotic inverse spectral problem for anharmonic oscillators." Communications in Mathematical Physics 112, no. 3 (September 1987): 491–502. http://dx.doi.org/10.1007/bf01218488.

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22

Yu, Dan. "Asymptotic behavior of bootstrap spectral window estimation." Acta Mathematicae Applicatae Sinica 13, no. 2 (April 1997): 123–29. http://dx.doi.org/10.1007/bf02015133.

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23

Mitrokhin, Sergey I. "On the study of the spectral properties of diﬀerential operators with a smooth weight function." Russian Universities Reports. Mathematics, no. 129 (2020): 25–47. http://dx.doi.org/10.20310/2686-9667-2020-25-129-25-47.

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In this paper we study the spectral properties of a third-order diﬀerential operator with a summable potential with a smooth weight function. The boundary conditions are separated. The method of studying diﬀerential operators with summable potential is a development of the method of studying operators with piecewise smooth coeﬃcients. Boundary value problems of this kind arise in the study of vibrations of rods, beams and bridges composed of materials of diﬀerent densities. The diﬀerential equation deﬁning the diﬀerential operator is reduced to the solution of the Volterra integral equation by means of the method of variation of constants. The solution of the integral equation is found by the method of successive Picard approximations. Using the study of an integral equation, we obtained asymptotic formulas and estimates for the solutions of a diﬀerential equation deﬁning a diﬀerential operator. For large values of the spectral parameter, the asymptotics of solutions of the diﬀerential equation that deﬁnes the diﬀerential operator is derived. Asymptotic estimates of solutions of a diﬀerential equation are obtained in the same way as asymptotic estimates of solutions of a diﬀerential operator with smooth coeﬃcients. The study of boundary conditions leads to the study of the roots of the function, presented in the form of a third-order determinant. To get the roots of this function, the indicator diagram wasstudied. The roots of this equation are in three sectors of an inﬁnitely small size, given by the indicator diagram. The article studies the behavior of the roots of this equation in each of the sectors of the indicator diagram. The asymptotics of the eigenvalues of the diﬀerential operator under study is calculated. The formulas found for the asymptotics of eigenvalues allow us to study the spectral properties of the eigenfunctions of the diﬀerential operator under study.

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24

Soon-Sen Lau, P. J. Sherman, and L. B. White. "Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra." IEEE Transactions on Information Theory 48, no. 4 (April 2002): 909–17. http://dx.doi.org/10.1109/18.992779.

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25

Kalimbetov, Burkhan, Valeriy Safonov, and Dinara Zhaidakbayeva. "Asymptotic Solution of a Singularly Perturbed Integro-Differential Equation with Exponential Inhomogeneity." Axioms 12, no. 3 (February 27, 2023): 241. http://dx.doi.org/10.3390/axioms12030241.

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The integro-differential Cauchy problem with exponential inhomogeneity and with a spectral value that turns zero at an isolated point of the segment of the independent variable is considered. The problem belongs to the class of singularly perturbed equations with an unstable spectrum and has not been considered before in the presence of an integral operator. A particular difficulty is its investigation in the neighborhood of the zero spectral value of inhomogeneity. Here, it is not possible to apply the well-known procedure of Lomov’s regularization method, so the authors have chosen the method of constructing the asymptotic solution of the initial problem based on the use of the regularized asymptotic solution of the fundamental solution of the corresponding homogeneous equation whose construction from the positions of the regularization method has not been considered so far. In the case of an unstable spectrum, it is necessary to take into account its point features. In this case, inhomogeneity plays an essential role. It significantly affects the type of singularities in the solution of the initial problem. The fundamental solution allows us to construct asymptotics regardless of the nature of the inhomogeneity (it can be both slowly changing and rapidly changing, for example, rapidly oscillating). The approach developed in the paper is universal with respect to arbitrary inhomogeneity. The first part of the study develops an algorithm for the regularization method to construct the asymptotic (of any order on the parameter) of the fundamental solution of the corresponding homogeneous integro-differential equation. The second part is devoted to constructing the asymptotics of the solution of the original problem. The main asymptotic term is constructed in detail, and the possibility of constructing its higher terms is pointed out. In the case of a stable spectrum, we can construct regularized asymptotics without using a fundamental solution.

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26

Молчанова, Е. А. "АСИМПТОТИЧЕСКОЕ МОДЕЛИРОВАНИЕ СПЕКТРАЛЬНОЙ ЗАДАЧИ." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 74 (2021): 12–18. http://dx.doi.org/10.17223/19988621/74/2.

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A mathematical model of a spectral problem containing a small parameter at the higher derivatives is investigated by an asymptotic method. The expected solution and its geometric parameters are presented as formal asymptotic decompositions. As a result, the original highorder differential task is reduced to a sequence of lower order tasks. Next, the zero approximation problem under the main boundary conditions is solved, the execution of which leads to a system of linear algebraic equations containing a spectral parameter. Equating to the zero of the determinant of the resulting system gives transcendent equations for eigenvalues. The asymptotic genesis of emerging transcendental equations allows asymptotic analysis to be applied to these equations. It helps to reveal the components of the equation that make the major contribution to the spectrum formation. Graphical solutions are used as leading considerations in this analysis. As a result of the asymptotic simulation, approximate formulas for the eigenvalues of the spectral problem have been obtained.

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27

Khiem, Nguyen Tien. "Spectral analysis of vibration in weakly non-linear systems." Vietnam Journal of Mechanics 22, no. 3 (September 30, 2000): 181–92. http://dx.doi.org/10.15625/0866-7136/9974.

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The weakly nonlinear systems subjected to deterministic excitations have been fully and deeply studied by use of the well developed asymptotic methods [1-4]. The systems excited by a random load have been investigated mostly using the Fokker-Plank-Kolmogorov equation technique combined with the asymptotic methods [5-8]. However, the last approach in most successful cases allows to obtain only a stationary single point probability density function, that contains no information about the correlation nor' consequently, the spectral structure of the response. The linearization technique [9, 10] in general permits the spectral density of the response to be determined, but the spectral function obtained by this method because of the linearization eliminates the effect of the nonlinearity. Thus, spectral structure of response of weakly nonlinear systems to random excitation, to the author's knowledge, has not been studied enough. This paper deals with the above mentioned problem. The main idea of this work is the use of an analytical simulation of random excitation given by its spectral density function and afterward application of the well known procedure of the asymptotic method to obtain an asymptotic expression of the response spectral density function. The obtained spectral relationship covers the linear system case and especially emphasizes the nonlinear effect on the spectral density of response. The theory will be illustrated by an example and at the end of this paper there will be a discussion about the obtained results.

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28

Dehghani Tazehkand, I., and A. Jodayree Akbarfam. "An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph." ISRN Applied Mathematics 2012 (May 27, 2012): 1–23. http://dx.doi.org/10.5402/2012/132842.

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We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

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29

GÉRARD, C., and A. PANATI. "SPECTRAL AND SCATTERING THEORY FOR SOME ABSTRACT QFT HAMILTONIANS." Reviews in Mathematical Physics 21, no. 03 (April 2009): 373–437. http://dx.doi.org/10.1142/s0129055x09003645.

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We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form H = dΓ(ω) + V acting on the bosonic Fock space Γ(𝔥), where ω is a massive one-particle Hamiltonian acting on 𝔥 and V is a Wick polynomial Wick(w) for a kernel w satisfying some decay properties at infinity. We describe the essential spectrum of H, prove a Mourre estimate outside a set of thresholds and prove the existence of asymptotic fields. Our main result is the asymptotic completeness of the scattering theory, which means that the CCR representations given by the asymptotic fields are of Fock type, with the asymptotic vacua equal to the bound states of H. As a consequence, H is unitarily equivalent to a collection of second quantized Hamiltonians.

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30

Binding, Paul, and Patrick J. Browne. "Spectral properties of two parameter eigenvalue problems II." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 106, no. 1-2 (1987): 39–51. http://dx.doi.org/10.1017/s0308210500018187.

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SynopsisWe consider eigenvalues λ =(λ1, λ2) ∈R2 for the problem W(λ)x = 0, x ≠ 0, x ∈ H, where W(λ) = R + λ1V1 + λ2V2), and R, V1, V2 are self-adjoint operators on a separable Hilbert space H, R being bounded below with compact resolvent and V1, V2 being bounded. The i-th eigencurve Z1 is the set of eigenvalues λ, for which the i-th eigenvalue (counted according to multiplicity and in increasing order) of W(λ) vanishes. We study monotonic and asymptotic properties of Zi, and we give formulae for any asymptotes that exist. Additional results are given in the finite dimensional case.

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31

Zayed, E. M. E. "Eigenvalues of the negative Laplacian for arbitrary multiply connected domains." International Journal of Mathematics and Mathematical Sciences 19, no. 3 (1996): 581–86. http://dx.doi.org/10.1155/s0161171296000804.

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The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}−2asP→∞. Further results may be obtained.

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32

Nazarov, S. A., and J. Sokolowski. "On asymptotic analysis of spectral problems in elasticity." Latin American Journal of Solids and Structures 8, no. 1 (2011): 27–54. http://dx.doi.org/10.1590/s1679-78252011000100003.

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33

Tomášek, Ladislav. "ASYMPTOTIC SIMULTANEOUS CONFIDENCE BANDS FOR AUTOREGRESSIVE SPECTRAL DENSITY." Journal of Time Series Analysis 8, no. 4 (July 1987): 469–77. http://dx.doi.org/10.1111/j.1467-9892.1987.tb00009.x.

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34

Motamedi, Zohreh, and M. Reza Soleymani. "Asymptotic Spectral Efficiency of MIMO Ad hoc Networks." IEEE Transactions on Signal Processing 58, no. 1 (January 2010): 462–66. http://dx.doi.org/10.1109/tsp.2009.2028193.

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35

Mazzoleni, Dario, Benedetta Pellacci, and Gianmaria Verzini. "Asymptotic spherical shapes in some spectral optimization problems." Journal de Mathématiques Pures et Appliquées 135 (March 2020): 256–83. http://dx.doi.org/10.1016/j.matpur.2019.10.002.

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36

Martinez, Diane, and Jody Trout. "Asymptotic Spectral Measures, Quantum Mechanics, and E -Theory." Communications in Mathematical Physics 226, no. 1 (March 1, 2002): 41–60. http://dx.doi.org/10.1007/s002200200595.

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37

Shih, Mau-Hsiang, Jinn-Wen Wu, and Chin-Tzong Pang. "Asymptotic stability and generalized Gelfand spectral radius formula." Linear Algebra and its Applications 252, no. 1-3 (February 1997): 61–70. http://dx.doi.org/10.1016/0024-3795(95)00592-7.

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38

Janas, Jan, and Marcin Moszyński. "Spectral properties of Jacobi matrices by asymptotic analysis." Journal of Approximation Theory 120, no. 2 (February 2003): 309–36. http://dx.doi.org/10.1016/s0021-9045(02)00038-2.

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39

Räbiger, Frank, and Manfred P. H. Wolff. "Spectral and asymptotic properties of resolvent-dominated operators." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 2 (April 2000): 181–201. http://dx.doi.org/10.1017/s1446788700001944.

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AbstractLet A and B be (not necessarily bounded) linear operators on a Banach lattice E such that |(s – B)-1x|≤ (s – A)-1|x| for all x in E and sufficiently large s ∈ R. The main purpose of this paper is to investigate the relation between the spectra σ(B) and σ(A) of B and A, respectively. We apply our results to study asymptotic properties of dominated C0-semigroups.

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40

Kondej, Sylwia, and David Krejčiřík. "Asymptotic spectral analysis in colliding leaky quantum layers." Journal of Mathematical Analysis and Applications 446, no. 2 (February 2017): 1328–55. http://dx.doi.org/10.1016/j.jmaa.2016.09.032.

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41

Delcroix, Antoine, Jean-André Marti, and Michael Oberguggenberger. "Spectral asymptotic analysis in algebras of generalized functions." Asymptotic Analysis 59, no. 1-2 (2008): 83–107. http://dx.doi.org/10.3233/asy-2008-0885.

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42

Hameed, Ehsan, and Yahea Saleem. "On spectral asymptotic for the second-derivative operators." Journal of Physics: Conference Series 1591 (July 2020): 012057. http://dx.doi.org/10.1088/1742-6596/1591/1/012057.

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43

Bourget, Alain. "Spectral Asymptotic for the High-Dimensional Euler Top." Letters in Mathematical Physics 86, no. 1 (October 2008): 47–52. http://dx.doi.org/10.1007/s11005-008-0273-4.

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44

Štampach, František. "Asymptotic Spectral Properties of the Hilbert \(L\) -Matrix." SIAM Journal on Matrix Analysis and Applications 43, no. 4 (November 18, 2022): 1658–79. http://dx.doi.org/10.1137/22m1476794.

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45

Rubtsova, O. A., and V. N. Pomerantsev. "Spectral shift function for a discretized continuum." Journal of Physics A: Mathematical and Theoretical 55, no. 9 (February 4, 2022): 095301. http://dx.doi.org/10.1088/1751-8121/ac4b8c.

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Abstract A spectral shift function (SSF) is an important object in the scattering theory which is related both to the spectral density and to the scattering matrix. In the paper, it is shown how to employ the SSF formalism to solve scattering problems when the continuum is discretized, e.g. when solving a scattering problem in a finite volume or in the representation of some finite square-integrable basis. A new algorithm is proposed for reconstructing integrated densities of states and the SSF using a union of discretized spectra corresponding to a set of Gaussian bases with the shifted scale parameters. The examples given show that knowledge of the discretized spectra of the total and asymptotic Hamiltonians is sufficient to find the scattering partial phase shifts at any required energy, as well as the resonances parameters.

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46

Xu, Houbao, Weihua Guo, Jingyuan Yu, and Guangtian Zhu. "Asymptotic stability of a repairable system with imperfect switching mechanism." International Journal of Mathematics and Mathematical Sciences 2005, no. 4 (2005): 631–43. http://dx.doi.org/10.1155/ijmms.2005.631.

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This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positiveC0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and0is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue0.

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47

Jin, Xue-Lian, Yan Li, and Fu Zheng. "Spectrum and Stability of a 1-d Heat-Wave Coupled System with Dynamical Boundary Control." Mathematical Problems in Engineering 2019 (June 4, 2019): 1–9. http://dx.doi.org/10.1155/2019/5716729.

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In this paper, the negative proportional dynamic feedback is designed in the right boundary of the wave component of the 1-d heat-wave system coupled at the interface and the long-time behavior of the system is discussed. The system is formulated into an abstract Cauchy problem on the energy space. The energy of the system does not increase because the semigroup generated by the system operator is contracted. In the meanwhile, the asymptotic stability of the system is derived in light of the spectral configuration of the system operator. Furthermore, the spectral expansions of the system operator are precisely investigated and the asymptotical stability is not exponential and is shown in view of the spectral expansions.

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48

Reese, Daniel R., Francisco Espinosa Lara, and Michel Rieutord. "Pulsations of rapidly rotating stars with compositional discontinuities." Proceedings of the International Astronomical Union 9, S301 (August 2013): 169–72. http://dx.doi.org/10.1017/s1743921313014270.

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AbstractRecent observations of rapidly rotating stars have revealed the presence of regular patterns in their pulsation spectra. This has raised the question as to their physical origin, and, in particular, whether they can be explained by an asymptotic frequency formula for low-degree acoustic modes, as recently discovered through numerical calculations and theoretical considerations. In this context, a key question is whether compositional/density gradients can adversely affect such patterns to the point of hindering their identification. To answer this question, we calculate frequency spectra using two-dimensional ESTER stellar models. These models use a multi-domain spectral approach, allowing us to easily insert a compositional discontinuity while retaining a high numerical accuracy. We analyse the effects of such discontinuities on both the frequencies and eigenfunctions of pulsation modes in the asymptotic regime. We find that although there is more scatter around the asymptotic frequency formula, the semi-large frequency separation can still be clearly identified in a spectrum of low-degree acoustic modes.

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49

Zabroda, O. N., and I. B. Simonenko. "Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions." Functional Analysis and Its Applications 38, no. 1 (January 2004): 65–66. http://dx.doi.org/10.1023/b:faia.0000024869.01751.f0.

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50

Amırov, Rauf Kh, and A. Adiloglu Nabıev. "Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/361989.

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In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.

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