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1.

図書
図書
1. Matrices and compact operators
F.V. Atkinson
出版情報: New York : Academic Press, c1972  xi, 209 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 82-1 . Multiparameter eigenvalue problems / [by] F.V. Atkinson ; v. 1
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2.

図書
図書
2. Eigenvalue distribution of compact operators
Hermann König
出版情報: Basel ; Boston : Birkhäuser Verlag, 1986  262 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 16
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3.

図書
図書
3. Microlocal analysis and precise spectral asymptotics
Victor Ivrii
出版情報: Berlin ; New York : Springer, c1998  xv, 731 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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4.

図書
図書
4. The bispectral problem
John Harnad, Alex Kasman, editors
出版情報: Providence, R.I. : American Mathematical Society, c1998  viii, 235 p. ; 26 cm
シリーズ名: CRM proceedings & lecture notes ; v. 14
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目次情報: 続きを見る
Bispectrality: Automorphisms of the Weyl algebra and bispectral operators / B. Bakalov ; E. Horozov ; M. YakimovPart 1：
Huygens' principle and the bispectral problem / Y. Berest
Some bispectral musings / F. A. Grunbaum
Beyond the classical orthogonal polynomials / L. Haine
Bispectral operators, dual isomondromic deformations and the Riemann-Hilbert dressing method / J. Harnad
Darboux transformations and the bispectral problem / A. Kasman
The discrete version of the bispectral problem / F. Levstein ; L. F. Matusevich
Explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs / M. Rothstein
Bispectrality and Darboux transformations in the theory of orthogonal polynomials / V. Spiridonov ; L. Vinet ; A. Zhedanov
Baker-Akhiezer functions and the bispectral problem in many dimensions / A. P. Veselov
Bispectral algebras of ordinary differential operators / G. Wilson
The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems / J. P. Zubelli
Related Topics: The geometry of spinors and the multicomponent BKP and DKP hierarchies / V. Kac ; J. van de LeurPart 2：
The Hamiltonian route to Sato Grassmannian / F. Magri
Darboux transformations in associative rings and functional-difference equations / V. B. Matveev
Remarks about the Calogero-Moser system and the KP equation / A. Y. Orlov
Subject index
Bispectrality: Automorphisms of the Weyl algebra and bispectral operators / B. Bakalov ; E. Horozov ; M. YakimovPart 1：
Huygens' principle and the bispectral problem / Y. Berest
Some bispectral musings / F. A. Grunbaum
5.

図書
図書
5. Eigenvalues and s-numbers
Albrecht Pietsch
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987  360 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 13
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6.

図書
図書
6. Two-parameter eigenvalue problems in ordinary differential equations (: uk ; : us)
M. Faierman
出版情報: Harlow, Essex, England : Longman Scientific & Technical , New York : Wiley, 1991  160 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 205
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7.

図書
図書
7. Spectral theory of ordinary differential operators (Ellis Horwood ; Halsted press)
Erich Müller-Pfeiffer ; translation editor, M.S.P. Eastham
出版情報: Chichester : E. Horwood , New York : Halsted Press [distributor], 1981  246 p. ; 24 cm
シリーズ名: Ellis Horwood series in mathematics and its applications
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8.

図書
図書
8. Asymptotic distribution of eigenvalues of differential operators
by Serge Levendorskiĭ
出版情報: Dordrecht [Netherlands] ; Boston : Kluwer Academic Publishers, c1990  xviii, 279 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 53
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9.

図書
図書
9. Methods of intermediate problems for eigenvalues : theory and ramifications
Alexander Weinstein and William Stenger
出版情報: New York : Academic Press, 1972  xi, 236 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 89
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目次情報: 続きを見る
Preface
Overview / 1：
Methods of Operator Approximation in System Modelling / I：
Nonlinear Operator Approximation with Preassigned Accuracy / 2：
Introduction / 2.1：
Generic formulation of the problem / 2.2：
Operator approximation in space C([0; 1]) / 2.3：
Operator approximation in Banach spaces by polynomial operators / 2.4：
Approximation on compact sets in topological vector spaces / 2.5：
Approximation on noncompact sets in Hilbert spaces / 2.6：
Special results for maps into Banach spaces / 2.7：
Concluding remarks / 2.8：
Interpolation of Nonlinear Operators 65 / 3：
Lagrange interpolation in Banach spaces / 3.1：
Weak interpolation of nonlinear operators / 3.3：
Some related results / 3.4：
Realistic Operators and their Approximation / 3.5：
Formalization of concepts related to description of real-world objects / 4.1：
Approximation of RÂícontinuous operators / 4.3：
Methods of Best Approximation for Nonlinear Operators / 4.4：
Best Approximation of nonlinear operators in Banach spaces: Deterministic case / 5.1：
Estimation of mean and covariance matrix for random vectors / 5.3：
Best Hadamard-quadratic approximation / 5.4：
Best polynomial approximation / 5.5：
Best causal approximation / 5.6：
Best hybrid approximations / 5.7：
Optimal Estimation of Random Vectors / 5.8：
Computational Methods for Optimal Filtering of Stochastic Signals / 6：
Optimal linear Filtering in Finite dimensional vector spaces / 6.1：
Optimal linear Filtering in Hilbert spaces / 6.3：
Optimal causal linear Filtering with piecewise constant memory / 6.4：
Optimal causal polynomial Filtering with arbitrarily variable memory / 6.5：
Optimal nonlinear Filtering with no memory constraint / 6.6：
Computational Methods for Optimal Compression and Reconstruction of Random Data / 6.7：
Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) / 7.1：
Rank-constrained matrix approximations / 7.3：
Generic PCA{KLT / 7.4：
Optimal hybrid transform based on Hadamard-quadratic approximation / 7.5：
Optimal transform formed by a combination of nonlinear operators / 7.6：
Optimal generalized hybrid transform / 7.7：
Bibliography / 7.8：
Index
Preface
Overview / 1：
Methods of Operator Approximation in System Modelling / I：
10.

図書
図書
10. Matrix theory and its applications : selected topics
N.J. Pullman
出版情報: New York : M. Dekker, c1976  vi, 240 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 35
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11.

図書
図書
11. Numerical and quantitative analysis
G. Fichera ; translated from the Italian by Sandro Graffi
出版情報: London ; San Francisco : Pitman, 1978  x, 208 p. ; 26 cm
シリーズ名: Surveys and reference works in mathematics / main editors, A. Jeffrey, R.G. Douglas ; 3
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12.

図書
図書
12. Eigenvalues in Riemannian geometry
Isaac Chavel ; with a chapter by Burton Randol ; with appendix by Jozef Dodziuk
出版情報: Orlando ; Tokyo : Academic Press, 1984  xiv, 362 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 115
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目次情報: 続きを見る
Preface
The Laplacian
The Basic Examples
Curvature
Isoperimetric Inequalities
Eigenvalues and Kinematic Measure
The Heat Kernel for Compact Manifolds
The Dirichlet Heat Kernel for Regular Domains
The Heat Kernel for Noncompact Manifolds
Topological Perturbations with Negligible Effect
Surfaces of Constant Negative Curvature
The Selberg Trace Formula
Miscellanea
Laplacian on Forms
Bibliography
Index
Preface
The Laplacian
The Basic Examples
13.

図書
図書
13. Eigenvalues of matrices
Françoise Chatelin ; with exercises by Mario Ahués and Françoise Chatelin ; translated with additional material by Walter Ledermann
出版情報: New York ; Chichester : Wiley & Sons, c1993  xviii, 382 p. ; 24 cm
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14.

図書
図書
14. Nonlinear hyperbolic equations, spectral theory, and wavelet transformations : a volume of advances in partial differential equations (:us ; :sz)
Sergio Albeverio ... [et al], editors
出版情報: Basel : Birkhäuser, c2003  [vii], 437 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 145
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15.

図書
図書
15. Spectral generalizations of line graphs : on graphs with least eigenvalue -2 (: pbk)
Dragoš Cvetković, Peter Rowlinson, Slobodan Simić
出版情報: Cambridge, U.K. : Cambridge University Press, 2004  xi, 298 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 314
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16.

図書
図書
16. Geršgorin and his circles
Richard S. Varga
出版情報: Berlin : Springer, c2004  x, 226 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 36
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目次情報: 続きを見る
Preface / I：
Basic Theory / 1：
Geršgorin's Theorem / 1.1：
Extensions of Geršgorin's Theorem via Graph Theory / 1.2：
Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3：
A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4：
Geršgorin-Type Eigenvalue Inclusion Theorems / 2：
Brauer's Ovals of Cassini / 2.1：
Higher-Order Lemniscates / 2.2：
Comparison of the Brauer Sets and the Brualdi Sets / 2.3：
The Sharpness of Brualdi Lemniscate Sets / 2.4：
An Example / 2.5：
More Eigenvalue Inclusion Results / 3：
The Parodi-Schneider Eigenvalue Inclusion Sets / 3.1：
The Field of Values of a Matrix / 3.2：
Newer Eigenvalue Inclusion Sets / 3.3：
The Pupkov-Solov'ev Eigenvalue Inclusions Set / 3.4：
Minimal Geršgorin Sets and Their Sharpness / 4：
Minimal Geršgorin Sets / 4.1：
Minimal Geršgorin Sets via Permutations / 4.2：
A Comparison of Minimal Geršgorin Sets and Brualdi Sets / 4.3：
G-Functions / 5：
The Sets <$>{\cal F}_{\bf n}<$> and <$>{\cal G}_{\bf n}<$> / 5.1：
Structural Properties of <$>{\cal G}_{\bf n}<$> and <$>{\cal G}_{\bf n}^{\bf c}<$> / 5.2：
Minimal G-Functions / 5.3：
Minimal G-Functions with Small Domains of Dependence / 5.4：
Connections with Brauer Sets and Generalized Brualdi Sets / 5.5：
Geršgorin-Type Theorems for Partitioned Matrices / 6：
Partitioned Matrices and Block Diagonal Dominance / 6.1：
A Different Norm Approach / 6.2：
A Variation on a Theme by Brualdi / 6.3：
G-Functions in the Partitioned Case / 6.4：
Geršgorin's Paper from 1931, and Comments / Appendix A：
Vector Norms and Induced Operator Norms / Appendix B：
The Perron-Frobenius Theory of Nonnegative Matrices / Appendix C：
Matlab 6 Programs / Appendix D：
References
Preface / I：
Basic Theory / 1：
Geršgorin's Theorem / 1.1：
17.

図書
図書
17. The asymptotic distribution of eigenvalues of partial differential operators
Yu. Safarov, D. Vassiliev
出版情報: Providence, R.I. : American Mathematical Society, c1997  xiii, 354 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 155
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目次情報: 続きを見る
Main results
Oscillatory integrals
Construction of the wave group
Singularities of the wave group
Proof of main results
Mechanical applications
Spectral problem on the half-line / Appendix A：
Fourier Tauberian theorems / Appendix B：
Stationary phase formula / Appendix C：
Hamiltonian billiards: proofs / Appendix D：
Factorization of smooth functions and Taylor-type formulae / Appendix E：
References
Principal notation
Index
Main results
Oscillatory integrals
Construction of the wave group
18.

図書
図書
18. Perturbation theory of eigenvalue problems
Franz Rellich ; assisted by J. Berkowitz
出版情報: New York : Gordon and Breach, c1969  x, 127 p. ; 24 cm
シリーズ名: Notes on mathematics and its applications
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