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1.

図書

図書
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:
2.

図書

図書
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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3.

図書

図書
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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4.

図書

図書
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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5.

図書

図書
Yousef Saad
出版情報: Philadelphia : Society for Industrial and Applied Mathematics(SIAM), c2011  xvi, 276 p. ; 23 cm
シリーズ名: Classics in applied mathematics ; 66
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目次情報: 続きを見る
Preface to the Classics Edition
Preface
Background in matrix theory and linear algebra / 1:
Sparse matrices / 2:
Perturbation theory and error analysis / 3:
The tools of spectral approximation / 4:
Subspace iteration / 5:
Krylov subspace methods / 6:
Filtering and restarting techniques / 7:
Preconditioning techniques / 8:
Non-standard eigenvalue problems / 9:
Origins of matrix eigenvalue problems / 10:
References
Index
Preface to the Classics Edition
Preface
Background in matrix theory and linear algebra / 1:
6.

図書

図書
Victor Ivrii
出版情報: Berlin ; New York : Springer-Verlag, 1984  v, 238 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1100
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7.

図書

図書
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
8.

図書

図書
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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9.

図書

図書
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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10.

図書

図書
Michihiro Kitahara
出版情報: Amsterdam ; Tokyo : Elsevier, 1985  viii, 281 p. ; 25 cm
シリーズ名: Studies in applied mechanics ; 10
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11.

図書

図書
S.S.M. Wong
出版情報: New York : Oxford University Press, 1986  ix, 241 p. ; 24 cm
シリーズ名: Oxford studies in nuclear physics
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目次情報: 続きを見る
Introduction / 1:
Random Matrix Studies / 2:
Energy Levels and Excitation Strengths / 3:
Simple Averages and their Propagation / 4:
Diagrammatic Method and Scalar Averaging / 5:
Configuration Averaging / 6:
Isospin Projection / 7:
Spin and Isospin / 8:
Irreducible Representations of Groups / 9:
Applications Appendices / 10:
References
Notation
Index
Introduction / 1:
Random Matrix Studies / 2:
Energy Levels and Excitation Strengths / 3:
12.

図書

図書
Pierre H. Bérard ; with an appendix by G. Besson
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  xiii, 272 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1207
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13.

図書

図書
H. Leipholz
出版情報: Leyden : Noordhoff International Publishing, [1977]  viii, 246 p. ; 23 cm
シリーズ名: Monographs and textbooks on mechanics of solids and fluids ; 5
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14.

図書

図書
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:
15.

図書

図書
Hans Volkmer
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  vi, 157 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1356
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16.

図書

図書
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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17.

図書

図書
I.I. Hirschman, Jr., Daniel Hughes
出版情報: Berlin ; New York : Springer-Verlag, 1977  145 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 618
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18.

図書

図書
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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19.

図書

図書
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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20.

図書

図書
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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21.

図書

図書
Charles Rockland
出版情報: Berlin ; New York : Springer-Verlag, 1975  171 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 464
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22.

図書

図書
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
23.

図書

図書
Beresford N. Parlett
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1980  xix, 348 p. ; 24 cm
シリーズ名: Prentice-Hall series in computational mathematics
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24.

図書

図書
Charles R. Johnson, Carlos M. Saiago
出版情報: Cambridge : Cambridge University Press, 2018  xxii, 291 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 211
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25.

図書

図書
Jürgen vom Scheidt, Walter Purkert
出版情報: New York : North Holland, c1983  271 p. ; 24 cm
シリーズ名: North Holland series in probability and applied mathematics
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26.

図書

図書
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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27.

図書

図書
Antoine Henrot
出版情報: Basel : Birkhäuser Verlag, 2006  x, 202 p. ; 24 cm
シリーズ名: Frontiers in mathematics
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目次情報: 続きを見る
Preface
Eigenvalues of elliptic operators / 1:
Notation and prerequisites / 1.1:
Notation and Sobolev spaces / 1.1.1:
Partial differential equations / 1.1.2:
Eigenvalues and eigenfunctions / 1.2:
Abstract spectral theory / 1.2.1:
Application to elliptic operators / 1.2.2:
First Properties of eigenvalues / 1.2.3:
Regularity of eigenfunctions / 1.2.4:
Some examples / 1.2.5:
Fredholm alternative / 1.2.6:
Min-max principles and applications / 1.3:
Min-max principles / 1.3.1:
Monotonicity / 1.3.2:
Nodal domains / 1.3.3:
Perforated domains / 1.4:
Tools / 2:
Schwarz rearrangement / 2.1:
Steiner symmetrization / 2.2:
Definition / 2.2.1:
Properties / 2.2.2:
Continuous Steiner symmetrization / 2.2.3:
Continuity of eigenvalues / 2.3:
Introduction / 2.3.1:
Continuity with variable coefficients / 2.3.2:
Continuity with variable domains (Dirichlet case) / 2.3.3:
The case of Neumann eigenvalues / 2.3.4:
Two general existence theorems / 2.4:
Derivatives of eigenvalues / 2.5:
Derivative with respect to the domain / 2.5.1:
Case of multiple eigenvalues / 2.5.3:
Derivative with respect to coefficients / 2.5.4:
The first eigenvalue of the Laplacian-Dirichlet / 3:
The Faber-Krahn inequality / 3.1:
The case of polygons / 3.3:
An existence result / 3.3.1:
The cases N = 3,4 / 3.3.2:
A challenging open problem / 3.3.3:
Domains in a box / 3.4:
Multi-connected domains / 3.5:
The second eigenvalue of the Laplacian-Dirichlet / 4:
Minimizing λ2 / 4.1:
The Theorem of Krahn-Szegö / 4.1.1:
Case of a connectedness constraint / 4.1.2:
A convexity constraint / 4.2:
Optimality conditions / 4.2.1:
Geometric properties of the optimal domain / 4.2.2:
Another regularity result / 4.2.3:
The other Dirichlet eigenvalues / 5:
Connectedness of minimizers / 5.1:
Existence of a minimizer for λ3 / 5.3:
A concentration-compactness result / 5.3.1:
Existence of a minimizer / 5.3.2:
Case of higher eigenvalues / 5.4:
Functions of Dirichlet eigenvalues / 6:
Ratio of eigenvalues / 6.1:
The Ashbaugh-Benguria Theorem / 6.2.1:
Some other ratios / 6.2.2:
A collection of open problems / 6.2.3:
Sums of eigenvalues / 6.3:
Sums of inverses / 6.3.1:
General functions of λ1 and λ2 / 6.4:
Description of the set ϵ = (λ1, λ2) / 6.4.1:
Existence of minimizers / 6.4.2:
Other boundary conditions for the Laplacian / 7:
Neumann boundary condition / 7.1:
Maximization of the second Neumann eigenvalue / 7.1.1:
Some other problems / 7.1.3:
Robin boundary condition / 7.2:
The Bossel-Daners Theorem / 7.2.1:
Optimal insulation of conductors / 7.2.3:
Stekloff eigenvalue problem / 7.3:
Eigenvalues of Schrödinger operators / 8:
Notation / 8.1:
A general existence result / 8.1.2:
Maximization or minimization of the first eigenvalue / 8.2:
The maximization problem / 8.2.1:
The minimization problem / 8.2.3:
Maximization or minimization of other eigenvalues / 8.3:
Maximization or minimization of the fundamental gap λ2 - λ1 / 8.4:
Single-well potentials / 8.4.1:
Minimization or maximization with an L constraint / 8.4.3:
Minimization or maximization with an Lp constraint / 8.4.4:
Maximization of ratios / 8.5:
Maximization of λ2(V)/λ1(V) in one dimension / 8.5.1:
Maximization of λn(V)/λ1(V) in one dimension / 8.5.3:
Non-homogeneous strings and membranes / 9:
Existence results / 9.1:
A first general existence result / 9.2.1:
A more precise existence result / 9.2.2:
Nonlinear constraint / 9.2.3:
Minimizing or maximizing λk(ρ) in dimension 1 / 9.3:
Minimizing λk(ρ) / 9.3.1:
Maximizing λk(ρ) / 9.3.2:
Minimizing or maximizing λk(ρ) in higher dimension / 9.4:
Case of a ball / 9.4.1:
General case / 9.4.2:
Some extensions / 9.4.3:
Optimal conductivity / 10:
The one-dimensional case / 10.1:
Minimization or maximization of λk(σ) / 10.2.1:
Case of Neumann boundary conditions / 10.2.3:
The general case / 10.3:
The bi-Laplacian operator / 10.3.1:
The clamped plate / 11.1:
History / 11.2.1:
Notation and statement of the theorem / 11.2.2:
Proof of the Rayleigh conjecture in dimension N = 2, 3 / 11.2.3:
Buckling of a plate / 11.3:
The case of a positive eigenfunction / 11.3.1:
The last step in the proof / 11.3.3:
Non-homogeneous rod and plate / 11.4:
The optimal shape of a column / 11.4.2:
References
Index
Preface
Eigenvalues of elliptic operators / 1:
Notation and prerequisites / 1.1:
28.

図書

図書
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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29.

図書

図書
A.R. Gourlay, G.A. Watson
出版情報: London ; New York : Wiley, c1973  xi, 132 p ; 24 cm
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30.

図書

図書
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
31.

図書

図書
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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32.

図書

図書
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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33.

図書

図書
Oktay Veliev
出版情報: Cham : Springer, c2019  xii, 326 p. ; 25 cm
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