Relevant bibliographies by topics / Spectral asymptotic

Academic literature on the topic 'Spectral asymptotic'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Spectral asymptotic"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Spectral asymptotic"

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Zabroda, Olga Nikolaievna. "Generalized convolution operators and asymptotic spectral theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200602061.

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The dissertation contributes to the further advancement of the theory of various classes of discrete and continuous (integral) convolution operators. The thesis is devoted to the study of sequences of matrices or operators which are built up in special ways from generalized discrete or continuous convolution operators. The generating functions depend on three variables and this leads to considerably more complicated approximation sequences. The aim was to obtain for each case a result analogous to the first Szegö limit theorem providing the first order asymptotic formula for the spectra of regular convolutions.
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Mascarenhas, Helena. "Convolution type operators on cones and asymptotic spectral theory." Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970638809.

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Rosenberger, Elke. "Asymptotic spectral analysis and tunnelling for a class of difference operators." Phd thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98050368X.

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Jacq, Thomas Soler. "Asymptotic spectral analysis of growing graphs and orthogonal matrix-valued polynomials." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/143939.

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Neste trabalho abordaremos a an alise espectral de grafos por dois estudos: técnicas de probabilidade quântica e por polinômios ortogonais com valores em matrizes. No Capítulo 1, consideraremos a matriz de adjacência do grafo tal como um operador linear e sua decomposição quântica permitir a uma an alise espectral que produzir a um teorema do limite central para tal grafo. No Capítulo 2, consideraremos uma medida com valores em matrizes induzida por polinômios ortogonais com valores em matrizes. Sob certas condições, e possível exibir explicitamente uma expressão de tal medida. Algumas aplicações em teoria dos grafos são dadas quando nos restringimos as matrizes estoc asticas e com valores em 0-1. Do nosso conhecimento, os cálculos e exemplos obtidos nas seçõoes 0.3.2, 0.3.3, 2.4 e 2.5 são novos.
In this work we focus on the spectral analysis of graphs via two studies: quantum probabilistic techniques and by orthogonal matrix-valued polynomials. In Chapter 1 we consider the adjacency matrix of a graph as a linear operator, and its quantum decomposition will allow a spectral analysis that will produce a central limit theorem for such graph. In Chapter 2, we consider a matrix-valued measure induced by orthogonal matrix-valued polynomials. Under certain conditions, it is possible to display an explicit expression for such measure. Some applications to combinatorics and graph theory are given when we restrict to the stochastic and 0-1 matrices. Up to our knowledge, the calculations and examples obtained in sections 0.3.2, 0.3.3, 2.4 and 2.5 are new.
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Hudson, Richard James Frederick. "Long memory spectral regression : an approach using generalised least squares." Thesis, Queensland University of Technology, 2002.

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Cherdantsev, Mikhail. "Asymptotic analysis of some spectral problems in high contrast homogenisation and in thin domains." Thesis, University of Bath, 2008. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501494.

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We study the spectral properties of two problems involving small parameters. The first one is an eigenvalue problem for a divergence form elliptic operator Aε with high contrast periodic coefficients of period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of 'order one' size. The local perturbation of coefficients for such operator could result in emergence of localised waves in the gaps of the Floquet-Bloch spectrum. We prove that, for the so-called double porosity type scaling, the eigenfunctions decay exponentially at in infinity, uniformly in ε. Then, using the tools of twoscale convergence for high contrast homogenisation, we prove the strong twoscale convergence of the eigenfunctions of Aε to the eigenfunctions of a two-scale limit homogenised operator A₀ , consequently establishing 'asymptotic one-to-one correspondence' between the eigenvalues and the eigenfunctions of these two operators. We also prove by direct means the stability of the essential spectrum of the homogenised operator with respect to the local perturbation of its coefficients. That allows us to establish not only the strong two-scale resolvent convergence of Aε to A₀ but also the Hausdor convergence of the spectra of Aε to the spectrum of A₀ , preserving the multiplicity of the isolated eigenvalues. As the second problem we consider the eigenvalue problem for the Laplacian in a network of thin domains with Dirichlet boundary conditions. We construct an asymptotic solution to the problem using the method of matched asymptotic expansions to obtain appropriate boundary conditions for the terms of the asymptotics near the junctions of thin domains. We justify the asymptotics and prove the error bound of order h3=2 , where h is the width of thin domains.
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Pielaszkiewicz, Jolanta Maria. "On the asymptotic spectral distribution of random matrices : closed form solutions using free independence." Licentiate thesis, Linköping University, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-58181.

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The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. In this thesis we combine the results of the theory together with the idea of free independence introduced by Voiculescu (1985). Important theoretical part of the thesis consists of the introduction to Free probability theory, which justifies use of asymptotic freeness with respect to particular matrices as well as the use of Stieltjes and R-transform. Both transforms are presented together with their properties. The aim of thesis is to point out characterizations of those classes of the matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider all matrices which can be decomposed to the sum of asymptotically free independent summands. In particular, explicit calculations are performed in order to illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a matrix Q and generalize Marcenko and Pastur (1967) theorem. The matrix Q is defined as   where Xi is p × n matrix following a matrix normal distribution, Xi ~ Np,n(0, \sigma^2I, I). Finally, theorems pointing out classes of matrices Q which lead to closed formula for the asymptotic spectral distribution will be presented. Particularly, results for matrices with inverse Stieltjes transform, with respect to the composition, given by a ratio of polynomials of 1st and 2nd degree, are given.
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Pielaszkiewicz, Jolanta. "On the asymptotic spectral distribution of random matrices : Closed form solutions using free independence." Licentiate thesis, Linköpings universitet, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-92637.

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The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. In this thesis we combine the results of the theory together with the idea of free independence introduced by Voiculescu (1985). Important theoretical part of the thesis consists of the introduction to Free probability theory, which justifies use of asymptotic freeness with respect to particular matrices as well as the use of Stieltjes and R-transform. Both transforms are presented together with their properties. The aim of thesis is to point out characterizations of those classes of the matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider all matrices which can be decomposed to the sum of asymptotically free independent summands. In particular, explicit calculations are performed in order to illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a matrix Q and generalize Marcenko and Pastur (1967) theorem. The matrix Q is defined as   where Xi is p × n matrix following a matrix normal distribution, Xi ~ Np,n(0, \sigma^2I, I). Finally, theorems pointing out classes of matrices Q which lead to closed formula for the asymptotic spectral distribution will be presented. Particularly, results for matrices with inverse Stieltjes transform, with respect to the composition, given by a ratio of polynomials of 1st and 2nd degree, are given.
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Södergren, Anders. "Asymptotic Problems on Homogeneous Spaces." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-132645.

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This PhD thesis consists of a summary and five papers which all deal with asymptotic problems on certain homogeneous spaces. In Paper I we prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. All our results are given with precise estimates on the rates of convergence to equidistribution. Papers II and III are concerned with statistical problems on the space of n-dimensional lattices of covolume one. In Paper II we study the distribution of lengths of non-zero lattice vectors in a random lattice of large dimension. We prove that these lengths, when properly normalized, determine a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. In Paper III we complement this result by proving that the asymptotic distribution of the angles between the shortest non-zero vectors in a random lattice is that of a family of independent Gaussians. In Papers IV and V we investigate the value distribution of the Epstein zeta function along the real axis. In Paper IV we determine the asymptotic value distribution and moments of the Epstein zeta function to the right of the critical strip as the dimension of the underlying space of lattices tends to infinity. In Paper V we determine the asymptotic value distribution of the Epstein zeta function also in the critical strip. As a special case we deduce a result on the asymptotic value distribution of the height function for flat tori. Furthermore, applying our results we discuss a question posed by Sarnak and Strömbergsson as to whether there in large dimensions exist lattices for which the Epstein zeta function has no zeros on the positive real line.
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Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.

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Dissertation for the Degree of Doctor of Philosophy in Mathematics
Fundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UTA
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Books on the topic "Spectral asymptotic"

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Microlocal analysis and precise spectral asymptotics. Berlin: Springer-Verlag, 1998.

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Dodziuk, Józef. Spectral asymptotics on degenerating hyperbolic 3-manifolds. Providence, R.I: American Mathematical Society, 1998.

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Barnett, Alex, 1972 December 7- editor of compilation, ed. Spectral geometry. Providence, Rhode Islands: American Mathematical Society, 2012.

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Helffer, Bernard. Semi-classical analysis for the Schrödinger operator and applications. Berlin: Springer-Verlag, 1988.

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Ivrii, Victor. Microlocal Analysis and Precise Spectral Asymptotics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-12496-3.

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Dimassi, Mouez. Spectral asymptotics in the semi-classical limit. Cambridge, U.K: Cambridge University Press, 1999.

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Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications III. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30537-6.

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Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications II. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30541-3.

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Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30545-1.

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Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications I. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30557-4.

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Book chapters on the topic "Spectral asymptotic"

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Bouche, Daniel, Frédéric Molinet, and Raj Mittra. "Spectral Theory of Diffraction." In Asymptotic Methods in Electromagnetics, 209–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60517-8_4.

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van Neerven, Jan. "Spectral mapping theorems." In The Asymptotic Behaviour of Semigroups of Linear Operators, 25–71. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9206-3_2.

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Shubin, Mikhail A. "Asymptotic Behaviour of the Spectral Function." In Pseudodifferential Operators and Spectral Theory, 133–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56579-3_3.

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Novotny, Antonio André, and Jan Sokołowski. "Compound Asymptotic Expansions for Spectral Problems." In Topological Derivatives in Shape Optimization, 225–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35245-4_9.

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Shubin, Mikhail A. "Asymptotic Behaviour of the Spectral Function." In Springer Series in Soviet Mathematics, 126–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-96854-9_3.

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van Neerven, Jan. "Spectral bound and growth bound." In The Asymptotic Behaviour of Semigroups of Linear Operators, 1–24. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9206-3_1.

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Lim, S. C., and S. V. Muniandy. "Local Asymptotic Properties of Multifractional Brownian Motion." In Partial Differential Equations and Spectral Theory, 205–14. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_23.

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Nagel, Rainer. "Spectral and asymptotic properties of strongly continuous semigroups." In Semigroups of Linear and Nonlinear Operations and Applications, 225–40. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1888-0_12.

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Davis, Richard A., Keh-Shin Lii, and Dimitris N. Politis. "Asymptotic Normality, Strong Mixing and Spectral Density Estimates." In Selected Works of Murray Rosenblatt, 361–74. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-8339-8_33.

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Hassi, Seppo, Adrian Sandovici, Henk de Snoo, and Henrik Winkler. "One-dimensional Perturbations, Asymptotic Expansions, and Spectral Gaps." In Spectral Theory in Inner Product Spaces and Applications, 149–73. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-8911-6_8.

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Conference papers on the topic "Spectral asymptotic"

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Kadavankandy, Arun, and Romain Couillet. "Asymptotic Gaussian Fluctuations of Spectral Clustering Eigenvectors." In 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2019. http://dx.doi.org/10.1109/camsap45676.2019.9022474.

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Liang, Song, Nobuaki Obata, and Shuji Takahashi. "Asymptotic spectral analysis of generalized Erdős–Rényi random graphs." In Noncommutative Harmonic Analysis with Applications to Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc78-0-16.

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JIMÉNEZ-CASAS, A. "WELL POSEDNESS AND ASYMPTOTIC BEHAVIOUR OF A CLOSED LOOP THERMOSYPHON." In Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701589_0004.

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Astapenko, Valery A. "Effect of charge exchange on atomic spectral line shapes in plasmas: Asymptotic theory." In The 15th international conference on spectral line shapes. AIP, 2001. http://dx.doi.org/10.1063/1.1370607.

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MICHAL, T., A. VERHOFF, and R. AGARWAL. "A characteristic based, asymptotic perturbation, spectral method forthe Euler equations." In 30th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-542.

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Mestre, Xavier, Roberto Pereira, and David Gregoratti. "Asymptotic Spectral Behavior of Kernel Matrices in Complex Valued Observations." In 2021 IEEE Data Science and Learning Workshop (DSLW). IEEE, 2021. http://dx.doi.org/10.1109/dslw51110.2021.9523410.

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AlAmmouri, Ahmad, Jeffrey G. Andrews, and Francois Baccelli. "Asymptotic Analysis of Area Spectral Efficiency in Dense Cellular Networks." In 2018 IEEE International Symposium on Information Theory (ISIT). IEEE, 2018. http://dx.doi.org/10.1109/isit.2018.8437555.

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Jwamer, Karwan, and Hawsar Ali. "ASYMPTOTIC BEHAVIORS OF THE SOLUTION AND EIGENVALUES OF SPECTRAL PROBLEM." In International Conference of Natural Science 2017. College of Basic Education, Charmo University, Chamchamal, Sulaimani/Iraq, 2018. http://dx.doi.org/10.31530/17013.

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Igarashi, Daisuke, and Nobuaki Obata. "Asymptotic spectral analysis of growing graphs: odd graphs and spidernets." In Quantum Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc73-0-18.

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Peng Pan, Youguang Zhang, Yuquan Sun, and Lie-Liang Yang. "Asymptotic Spectral-Efficiency of MIMO-CDMA Systems with Arbitrary Spatial Correlation." In 2011 IEEE Global Communications Conference (GLOBECOM 2011). IEEE, 2011. http://dx.doi.org/10.1109/glocom.2011.6133946.

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