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Books on the topic 'Spectral asymptotic'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

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

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2

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

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3

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

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4

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

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5

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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6

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

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7

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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8

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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9

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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10

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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11

Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications V. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30561-1.

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12

Sjöstrand, Johannes. Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10819-9.

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13

F, Warming Robert, and Ames Research Center, eds. The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1991.

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14

Birman, M., ed. Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/advsov/007.

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15

Spectral theory and geometric analysis: An international conference in honor of Mikhail Shubin's 65th birthday, July 29 - August 2, 2009, Northeastern University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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16

Holland, Paul V. The Human immunodeficiency virus and the spectrum of its infection: From asymptomatic antibody positive state toAcquired Immunodeficiency Syndrome (AIDS). Saluggia (Vercelli): Sorin Biomedica, 1986.

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17

United States. National Aeronautics and Space Administration., ed. Coordinated observations of interacting peculiar red giant binaries. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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18

Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman, and B. Prinari. Nonlinear wave equations: Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. Providence, Rhode Island: American Mathematical Society, 2015.

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19

Lectures on linear partial differential equations. Providence, R.I: American Mathematical Society, 2011.

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20

Semiclassical analysis. Providence, R.I: American Mathematical Society, 2012.

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21

Gilkey, Peter B. Asymptotic Formulae in Spectral Geometry. Taylor & Francis Group, 2003.

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22

Gilkey, Peter B. Asymptotic Formulae in Spectral Geometry. Taylor & Francis Group, 2003.

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23

Gilkey, Peter B. Asymptotic Formulae in Spectral Geometry. Taylor & Francis Group, 2003.

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24

Gilkey, Peter B. Asymptotic Formulae in Spectral Geometry. Taylor & Francis Group, 2003.

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25

Gilkey, Peter B. Asymptotic Formulae in Spectral Geometry. Taylor & Francis Group, 2003.

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26

Gilkey, Peter B. Asymptotic Formulae in Spectral Geometry. Taylor & Francis Group, 2003.

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27

Asymptotic Formulae in Spectral Geometry (Studies in Advanced Mathematics). Chapman & Hall/CRC, 2003.

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28

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8114-1.

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29

Non-Spectral Asymptotic Analysis of One-Parameter Operator Semigroups. Springer London, Limited, 2007.

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30

Tsai, Chung-Jun. Asymptotic spectral flow for Dirac operators of disjoint Dehn twists. 2011.

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31

Microlocal Analysis and Precise Spectral Asymptotics Springer Monographs in Mathematics. Springer, 2010.

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32

Birman, M. Sh. Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations (Advances in Soviet Mathematics, Vol 7). American Mathematical Society, 1991.

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33

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups (Operator Theory: Advances and Applications). Birkhäuser Basel, 2007.

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34

Ivrii, Victor. Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds with Boundary. Springer London, Limited, 2006.

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35

Helffer, Bernard. Semi-Classical Analysis for the Schrödinger Operator and Applications. Springer London, Limited, 2006.

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36

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation: Abstract. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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37

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves. American Mathematical Society, 2020.

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38

Sogge, Christopher D. Improved spectral asymptotics and periodic geodesics. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0005.

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This chapter proves an improved Weyl formula under the assumption that the set of periodic geodesics for (M,g) has measure zero. It then shows trace estimates associated with shrinking spectral bands, details and proves a lemma, and gives a related generalization of the Weyl formula from Chapter 3 that involves pseudodifferential operators. The chapter then proves its main result by using a version of the Duistermaat-Guillemin theorem, which allows the use of the Hadamard parametrix and the arguments from Chapter 3. To conclude, the chapter shows that one can improve the sup-norm estimates from Chapter 3 if one assumes a condition on the geodesic flow that is similar to a hypothesis laid out in the Duistermaat-Guillemin theorem.

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39

Ivrii, Victor. Microlocal Analysis and Precise Spectral Asymptotics. Springer, 2013.

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40

Zinn-Justin, Paul, and Jean-Bernard Zuber. Multivariate statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.28.

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This article considers some classical and more modern results obtained in random matrix theory (RMT) for applications in statistics. In the classic paradigm of parametric statistics, data are generated randomly according to a probability distribution indexed by parameters. From this data, which is by nature random, the properties of the deterministic (and unknown) parameters may be inferred. The ability to infer properties of the unknown Σ (the population covariance matrix) will depend on the quality of the estimator. The article first provides an overview of two spectral statistical techniques, principal components analysis (PCA) and canonical correlation analysis (CCA), before discussing the Wishart distribution and normal theory. It then describes extreme eigenvalues and Tracy–Widom laws, taking into account the results obtained in the asymptotic setting of ‘large p, large n’. It also analyses the results for the limiting spectra of sample covariance matrices..

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41

Sjostrand, J., and M. Dimassi. Spectral Asymptotics in the Semi-Classical Limit. Cambridge University Press, 2010.

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42

Sjostrand, J., and M. Dimassi. Spectral Asymptotics in the Semi-Classical Limit. Cambridge University Press, 2011.

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43

Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications II: Functional Methods and Eigenvalue Asymptotics. Springer, 2020.

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44

Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications II: Functional Methods and Eigenvalue Asymptotics. Springer, 2019.

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45

National Aeronautics and Space Administration (NASA) Staff. Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices. Independently Published, 2018.

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46

Sjöstrand, Johannes. Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations. Birkhäuser, 2019.

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47

Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications I: Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics. Springer International Publishing AG, 2020.

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48

Ivrii, Victor. Microlocal Analysis, Sharp Spectral Asymptotics and Applications I: Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics. Springer, 2019.

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49

Tirkkonen, Olav. Exact and Asymptotic Analysis of Largest Eigenvalue Based Spectrum Sensing. INTECH Open Access Publisher, 2012.

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50

Bouchaud, Jean-Phillipe, and Marc Potters. Asymptotic singular value distributions in information theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.41.

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This article examines asymptotic singular value distributions in information theory, with particular emphasis on some of the main applications of random matrices to the capacity of communication channels. Results on the spectrum of random matrices have been adopted in information theory. Furthermore, information theorists, motivated by certain channel models, have obtained a number of new results in random matrix theory (RMT). Most of those results are related to the asymptotic distribution of the (square of) the singular values of certain random matrices that model data communication channels. The article first provides an overview of three transforms that are useful in expressing the asymptotic spectrum results — Stieltjes transform, η-transform, and Shannon transform — before discussing the main results on the limit of the empirical distributions of the eigenvalues of various random matrices of interest in information theory.

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