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1.

図書

図書
Mark A. Pinsky
出版情報: Australia : Brooks/Cole, c2002  xviii, 376 p. ; 25 cm
シリーズ名: Brooks/Cole series in advanced mathematics
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目次情報: 続きを見る
Fourier Series on the Circle / 1:
Motivation and Heuristics / 1.1:
Motivation from Physics / 1.1.1:
The Vibrating String / 1.1.1.1:
Heat Flow in Solids / 1.1.1.2:
Absolutely Convergent Trigonometric Series / 1.1.2:
Examples of Factorial and Bessel Functions / 1.1.3:
Poisson Kernel Example / 1.1.4:
Proof of Laplace's Method / 1.1.5:
Nonabsolutely Convergent Trigonometric Series / 1.1.6:
Formulation of Fourier Series / 1.2:
Fourier Coefficients and Their Basic Properties / 1.2.1:
Fourier Series of Finite Measures / 1.2.2:
Rates of Decay of Fourier Coefficients / 1.2.3:
Piecewise Smooth Functions / 1.2.3.1:
Fourier Characterization of Analytic Functions / 1.2.3.2:
Sine Integral / 1.2.4:
Other Proofs That Si([infinity]) = 1 / 1.2.4.1:
Pointwise Convergence Criteria / 1.2.5:
Integration of Fourier Series / 1.2.6:
Convergence of Fourier Series of Measures / 1.2.6.1:
Riemann Localization Principle / 1.2.7:
Gibbs-Wilbraham Phenomenon / 1.2.8:
The General Case / 1.2.8.1:
Fourier Series in L[superscript 2] / 1.3:
Mean Square Approximation--Parseval's Theorem / 1.3.1:
Application to the Isoperimetric Inequality / 1.3.2:
Rates of Convergence in L[superscript 2] / 1.3.3:
Application to Absolutely-Convergent Fourier Series / 1.3.3.1:
Norm Convergence and Summability / 1.4:
Approximate Identities / 1.4.1:
Almost-Everywhere Convergence of the Abel Means / 1.4.1.1:
Summability Matrices / 1.4.2:
Fejer Means of a Fourier Series / 1.4.3:
Wiener's Closure Theorem on the Circle / 1.4.3.1:
Equidistribution Modulo One / 1.4.4:
Hardy's Tauberian Theorem / 1.4.5:
Improved Trigonometric Approximation / 1.5:
Rates of Convergence in C (T) / 1.5.1:
Approximation with Fejer Means / 1.5.2:
Jackson's Theorem / 1.5.3:
Higher-Order Approximation / 1.5.4:
Converse Theorems of Bernstein / 1.5.5:
Divergence of Fourier Series / 1.6:
The Example of du Bois-Reymond / 1.6.1:
Analysis via Lebesgue Constants / 1.6.2:
Divergence in the Space L[superscript 1] / 1.6.3:
Appendix: Complements on Laplace's Method / 1.7:
First Variation on the Theme-Gaussian Approximation / 1.7.0.1:
Second Variation on the Theme-Improved Error Estimate / 1.7.0.2:
Application to Bessel Functions / 1.7.1:
The Local Limit Theorem of DeMoivre-Laplace / 1.7.2:
Appendix: Proof of the Uniform Boundedness Theorem / 1.8:
Appendix: Higher-Order Bessel functions / 1.9:
Appendix: Cantor's Uniqueness Theorem / 1.10:
Fourier Transforms on the Line And Space / 2:
Basic Properties of the Fourier Transform / 2.1:
Riemann-Lebesgue Lemma / 2.2.1:
Approximate Identities and Gaussian Summability / 2.2.2:
Improved Approximate Identities for Pointwise Convergence / 2.2.2.1:
Application to the Fourier Transform / 2.2.2.2:
The n-Dimensional Poisson Kernel / 2.2.2.3:
Fourier Transforms of Tempered Distributions / 2.2.3:
Characterization of the Gaussian Density / 2.2.4:
Wiener's Density Theorem / 2.2.5:
Fourier Inversion in One Dimension / 2.3:
Dirichlet Kernel and Symmetric Partial Sums / 2.3.1:
Example of the Indicator Function / 2.3.2:
Dini Convergence Theorem / 2.3.3:
Extension to Fourier's Single Integral / 2.3.4.1:
Smoothing Operations in R[superscript 1]-Averaging and Summability / 2.3.5:
Averaging and Weak Convergence / 2.3.6:
Cesaro Summability / 2.3.7:
Approximation Properties of the Fejer Kernel / 2.3.7.1:
Bernstein's Inequality / 2.3.8:
One-Sided Fourier Integral Representation / 2.3.9:
Fourier Cosine Transform / 2.3.9.1:
Fourier Sine Transform / 2.3.9.2:
Generalized h-Transform / 2.3.9.3:
L[superscript 2] Theory in R[superscript n] / 2.4:
Plancherel's Theorem / 2.4.1:
Bernstein's Theorem for Fourier Transforms / 2.4.2:
The Uncertainty Principle / 2.4.3:
Uncertainty Principle on the Circle / 2.4.3.1:
Spectral Analysis of the Fourier Transform / 2.4.4:
Hermite Polynomials / 2.4.4.1:
Eigenfunction of the Fourier Transform / 2.4.4.2:
Orthogonality Properties / 2.4.4.3:
Completeness / 2.4.4.4:
Spherical Fourier Inversion in R[superscript n] / 2.5:
Bochner's Approach / 2.5.1:
Piecewise Smooth Viewpoint / 2.5.2:
Relations with the Wave Equation / 2.5.3:
The Method of Brandolini and Colzani / 2.5.3.1:
Bochner-Riesz Summability / 2.5.4:
A General Theorem on Almost-Everywhere Summability / 2.5.4.1:
Bessel Functions / 2.6:
Fourier Transforms of Radial Functions / 2.6.1:
L[superscript 2]-Restriction Theorems for the Fourier Transform / 2.6.2:
An Improved Result / 2.6.2.1:
Limitations on the Range of p / 2.6.2.2:
The Method of Stationary Phase / 2.7:
Statement of the Result / 2.7.1:
Proof of the Method of Stationary Phase / 2.7.2:
Abel's Lemma / 2.7.4:
Fourier Analysis in L[superscript p] Spaces / 3:
The M. Riesz-Thorin Interpolation Theorem / 3.1:
Generalized Young's Inequality / 3.2.0.1:
The Hausdorff-Young Inequality / 3.2.0.2:
Stein's Complex Interpolation Theorem / 3.2.1:
The Conjugate Function or Discrete Hilbert Transform / 3.3:
L[superscript p] Theory of the Conjugate Function / 3.3.1:
L[superscript 1] Theory of the Conjugate Function / 3.3.2:
Identification as a Singular Integral / 3.3.2.1:
The Hilbert Transform on R / 3.4:
L[superscript 2] Theory of the Hilbert Transform / 3.4.1:
L[superscript p] Theory of the Hilbert Transform, 1 [ p [ [infinity] / 3.4.2:
Applications to Convergence of Fourier Integrals / 3.4.2.1:
L[superscript 1] Theory of the Hilbert Transform and Extensions / 3.4.3:
Kolmogorov's Inequality for the Hilbert Transform / 3.4.3.1:
Application to Singular Integrals with Odd Kernels / 3.4.4:
Hardy-Littlewood Maximal Function / 3.5:
Application to the Lebesgue Differentiation Theorem / 3.5.1:
Application to Radial Convolution Operators / 3.5.2:
Maximal Inequalities for Spherical Averages / 3.5.3:
The Marcinkiewicz Interpolation Theorem / 3.6:
Calderon-Zygmund Decomposition / 3.7:
A Class of Singular Integrals / 3.8:
Properties of Harmonic Functions / 3.9:
General Properties / 3.9.1:
Representation Theorems in the Disk / 3.9.2:
Representation Theorems in the Upper Half-Plane / 3.9.3:
Herglotz/Bochner Theorems and Positive Definite Functions / 3.9.4:
Poisson Summation Formula And Multiple Fourier Series / 4:
The Poisson Summation Formula in R[superscript 1] / 4.1:
Periodization of a Function / 4.2.1:
Statement and Proof / 4.2.2:
Shannon Sampling / 4.2.3:
Multiple Fourier Series / 4.3:
Basic L[superscript 1] Theory / 4.3.1:
Pointwise Convergence for Smooth Functions / 4.3.1.1:
Representation of Spherical Partial Sums / 4.3.1.2:
Basic L[superscript 2] Theory / 4.3.2:
Restriction Theorems for Fourier Coefficients / 4.3.3:
Poisson Summation Formula in R[superscript d] / 4.4:
Simultaneous Nonlocalization / 4.4.1:
Application to Lattice Points / 4.5:
Kendall's Mean Square Error / 4.5.1:
Landau's Asymptotic Formula / 4.5.2:
Application to Multiple Fourier Series / 4.5.3:
Three-Dimensional Case / 4.5.3.1:
Higher-Dimensional Case / 4.5.3.2:
Schrodinger Equation and Gauss Sums / 4.6:
Distributions on the Circle / 4.6.1:
The Schrodinger Equation on the Circle / 4.6.2:
Recurrence of Random Walk / 4.7:
Applications to Probability Theory / 5:
Basic Definitions / 5.1:
The Central Limit Theorem / 5.2.1:
Restatement in Terms of Independent Random Variables / 5.2.1.1:
Extension to Gap Series / 5.3:
Extension to Abel Sums / 5.3.1:
Weak Convergence of Measures / 5.4:
An Improved Continuity Theorem / 5.4.1:
Another Proof of Bochner's Theorem / 5.4.1.1:
Convolution Semigroups / 5.5:
The Berry-Esseen Theorem / 5.6:
Extension to Different Distributions / 5.6.1:
The Law of the Iterated Logarithm / 5.7:
Introduction to Wavelets / 6:
Heuristic Treatment of the Wavelet Transform / 6.1:
Wavelet Transform / 6.2:
Wavelet Characterization of Smoothness / 6.2.0.1:
Haar Wavelet Expansion / 6.3:
Haar Functions and Haar Series / 6.3.1:
Haar Sums and Dyadic Projections / 6.3.2:
Completeness of the Haar Functions / 6.3.3:
Haar Series in C[subscript 0] and L[subscript p] Spaces / 6.3.3.1:
Pointwise Convergence of Haar Series / 6.3.3.2:
Construction of Standard Brownian Motion / 6.3.4:
Haar Function Representation of Brownian Motion / 6.3.5:
Proof of Continuity / 6.3.6:
Levy's Modulus of Continuity / 6.3.7:
Multiresolution Analysis / 6.4:
Orthonormal Systems and Riesz Systems / 6.4.1:
Scaling Equations and Structure Constants / 6.4.2:
From Scaling Function to MRA / 6.4.3:
Additional Remarks / 6.4.3.1:
Meyer Wavelets / 6.4.4:
From Scaling Function to Orthonormal Wavelet / 6.4.5:
Direct Proof that V[subscript 1] [minus sign in circle] V[subscript 0] Is Spanned by {[Psi](t - k)}[subscript k[set membership]Z] / 6.4.5.1:
Null Integrability of Wavelets Without Scaling Functions / 6.4.5.2:
Wavelets with Compact Support / 6.5:
From Scaling Filter to Scaling Function / 6.5.1:
Explicit Construction of Compact Wavelets / 6.5.2:
Daubechies Recipe / 6.5.2.1:
Hernandez-Weiss Recipe / 6.5.2.2:
Smoothness of Wavelets / 6.5.3:
A Negative Result / 6.5.3.1:
Cohen's Extension of Theorem 6.5.1 / 6.5.4:
Convergence Properties of Wavelet Expansions / 6.6:
Wavelet Series in L[superscript p] Spaces / 6.6.1:
Large Scale Analysis / 6.6.1.1:
Almost-Everywhere Convergence / 6.6.1.2:
Convergence at a Preassigned Point / 6.6.1.3:
Jackson and Bernstein Approximation Theorems / 6.6.2:
Wavelets in Several Variables / 6.7:
Two Important Examples / 6.7.1:
Tensor Product of Wavelets / 6.7.1.1:
General Formulation of MRA and Wavelets in R[superscript d] / 6.7.2:
Notations for Subgroups and Cosets / 6.7.2.1:
Riesz Systems and Orthonormal Systems in R[superscript d] / 6.7.2.2:
Scaling Equation and Structure Constants / 6.7.2.3:
Existence of the Wavelet Set / 6.7.2.4:
Proof That the Wavelet Set Spans V[subscript 1] [minus sign in circle] V[subscript 0] / 6.7.2.5:
Cohen's Theorem in R[superscript d] / 6.7.2.6:
Examples of Wavelets in R[superscript d] / 6.7.3:
References
Notations
Index
Fourier Series on the Circle / 1:
Motivation and Heuristics / 1.1:
Motivation from Physics / 1.1.1:
2.

図書

図書
edited by Mark A. Pinsky
出版情報: New York : M. Dekker, c1984  x, 460 p. ; 24 cm
シリーズ名: Advances in probability and related topics / edited by Peter Ney ; v. 7
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3.

図書

図書
edited by M.A. Pinsky
出版情報: Berlin ; New York : Springer-Verlag, 1975  vi, 162 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 451
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4.

図書

図書
Michael C. Cranston, Mark A. Pinsky, editors
出版情報: Providence, R.I. : American Mathematical Society, c1995  ix, 621 p. ; 26 cm
シリーズ名: Proceedings of symposia in pure mathematics ; v. 57
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目次情報: 続きを見る
Problems in Analysis: An improvement of the Osserman constant for the bass note of a drum / R. Banuelos ; T. CarrollPart I:
Heat content asymptotics for some open sets with a fractal boundary / M. van den
Berg On self-attracting random walks / E. Bolthausen ; U. Schmock
Positivity default for martingales and harmonic functions / J. Brossard
Optimal switching between two Brownian motions / R. Cairoli ; R. C. Dalang
Nonnegative solutions for semilinear elliptic equations with boundary conditions-a probabilistic approach / Z. Q. Chen ; R. J. Williams ; Z. Zhao
Simulated annealing and fastest cooling rates for some 1-dim spin glass models / T.-S. Chiang ; Y. Chow
Averaging stochastically perturbed Hamiltonian systems / T. G. Kurtz ; F. Marchetti
The interpretation and solution of ordinary differential equations driven by rough signals / T. J. Lyons
Time-reversal of the noisy Wiener-Hopf factorisation / L. C. G. Rogers
Some aspects of Brownian motion in a Poissonian potential / A.-S. Sznitman
Schrodinger operators and asymptotics for Poisson-Levy excursion measures for one-dimensional time-homogeneous diffusions / A. Truman ; D. Williams ; K. Y. Yu
Generalized arc-sine laws for one-dimensional diffusion processes and random walks / S. Watanabe
Problems in Geometry: Semimartingales with values in a Euclidean vector bundle and Ocone's formula on a Riemannian manifold / H. Airault ; P. MalliavinPart II:
Coupling constructions for hypoelliptic diffusions: Two examples / G. B. Arous ; M. Cranston ; W. S. Kendall
Heat kernel bounds on Riemannian manifolds / I. Benjamini ; I. Chavel ; E. A. Feldman
Brownian motion and harmonic functions on polygonal complexes / M. Brin ; Yu. Kifer
Heat kernel of a noncompact Riemannian manifold / A. Grigoryan
Flows and quasi-invariance of the Wiener measure on path spaces / E. P. Hsu
Levy's stochastic area formula and related problems / N. Ikeda ; S. Kusuoka ; S. Manabe
Markov processes and harmonic functions on hyperbolic metric spaces
Some problems concerning Levy processes on Lie groups / H. Kunita
The central limit theorem for geodesic flows on noncompact manifolds of constant negative curvature / Y. L. Jan
A renewal theorem for the distance in negative curvature / F. Ledrappier
A bootstrap proof of the limit theorem for linear SDE
Diffusion processes on a Lipschitz Riemannian manifold and their applications / W. Zheng
Infinite-Dimensional Problems: On path properties of super-2 processes. II / D. A. Dawson ; K. J. Hochberg ; V. VinogradovPart III:
Towards calculus and geometry on path spaces / B. K. Driver
Branching with a single point catalyst / E. B. Dynkin
The Brownian path-valued process and its connections with partial differential equations / J.-F. Le Gall
Inverse powers of white noise / Y. Hu ; T. Lindstrom ; B. Oksendal ; J. Uboe ; T. Zhang
Statistical mechanics of nonlinear wave equations / H. P. McKean ; K. L. Vaninsky
Markov properties for solutions of stochastic differential equations / D. Nualart
A quasihomeomorphism on the Wiener space / I. Shigekawa
Absolute continuity on the Wiener space and some applications / A. S. Ustunel ; M. Zakai
Invariant Gibbsian measures of the Klein-Gordon equation
Stochastic PDE/ Stochastic Flows: Dirichlet form methods for uniqueness of martingale problems and applications / S. Albeverio ; M. RocknerPart IV:
Anticipative problems in the theory of random dynamical systems / L. Arnold
Stability
Index for nonlinear stochastic differential equations / R. Z. Khasminskii
Degenerate stochastic differential equations, flows, and hypoellipticity / D. R. Bell ; S.-E. A. Mohammed
Derivative flows of stochastic differential equations: Moment exponents and geometric properties / K. D. Elworthy ; X.-M. Li
Invariant diffusion processes in Lie groups and stochastic flows / M. Liao
On stochastic integrals in topological vector spaces / R. Mikulevicius ; B. L. Rozovskii
Travelling waves for the KPP equation with noise / C. Mueller ; R. Sowers
Backward SDEs, quasilinear PDEs, and SPDEs / E. Pardoux
Invariance of the Lyapunov exponent under nonlinear perturbations / M. A. Pinsky
Problems in Analysis: An improvement of the Osserman constant for the bass note of a drum / R. Banuelos ; T. CarrollPart I:
Heat content asymptotics for some open sets with a fractal boundary / M. van den
Berg On self-attracting random walks / E. Bolthausen ; U. Schmock
5.

図書

図書
Mark A. Pinsky, Volker Wihstutz, editors
出版情報: Boston : Birkhäuser, 1992  viii, 346 p. ; 25 cm
シリーズ名: Progress in probability ; v. 27 . Diffusion processes and related problems in analysis / Mark A. Pinsky, Volker Wihstutz, editors ; v. 2
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6.

図書

図書
Mark A. Pinsky, editor
出版情報: Boston : Birkhäuser, 1990  xiii, 519 p. ; 24 cm
シリーズ名: Progress in probability ; v. 22 . Diffusion processes and related problems in analysis ; v. 1
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7.

図書

図書
Mark A. Pinsky
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1991  viii, 136 p. ; 23 cm
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