edited by Gunilla Borgefors, Rachid Deriche, Thomas S. Huang, Tianzi Jiang, Reinhard Klette, Ales Leonardis, Heinz-Otto Peitgen, Katsushi Ikeuchi, John K. Tsotsos, Isaac Amidror
1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums
10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions
11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series
13 A Partial Manuscript on Fourier and Laplace Transforms
14 Integral Analogues of Theta Functions adn Gauss Sums
15 Functional Equations for Products of Mellin Transforms
16 Infinite Products
17 A Preliminary Version of Ramanujan's Paper, On the Integral ∫_0^x tan^(-1)t)/t dt
18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis
20 Elementary Results
21 A Strange, Enigmatic Partial Manuscript.- Location Guide
Provenance
References
Index
Preface
1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums
10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions
Preface.- History of Quaternion and Clifford-Fourier Transforms and Wavelets
Part I: Quaternions.- 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis.- 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations.- 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals.- 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions.- 5 Bochner’s Theorems in the Framework of Quaternion Analysis.- 6 Bochner-Minlos Theorem and Quaternion Fourier Transform
Part II: Clifford Algebra.- 7 Square Roots of -1 in Real Clifford Algebras.- 8 A General Geometric Fourier Transform.- 9 Clifford-Fourier Transform and Spinor Representation of Images
10 Analytic Video (2D+t) Signals Using Clifford-Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras
11 Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications
12 Color Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising
13 Seeing the Invisible and Maxwell’s Equations
14 A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl_{0,n}
15 The Balian-Low theorem for the Windowed Clifford-Fourier Transform
16 Sparse Representation of Signals in Hardy Space. - Index
Preface.- History of Quaternion and Clifford-Fourier Transforms and Wavelets
Part I: Quaternions.- 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis.- 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations.- 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals.- 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions.- 5 Bochner’s Theorems in the Framework of Quaternion Analysis.- 6 Bochner-Minlos Theorem and Quaternion Fourier Transform
Part II: Clifford Algebra.- 7 Square Roots of -1 in Real Clifford Algebras.- 8 A General Geometric Fourier Transform.- 9 Clifford-Fourier Transform and Spinor Representation of Images
1 On Friedrichs commutators lemma for Hardy spaces and applications. Jorge Hounie
2 On the Hardy constant of some non-convex planar domains. Gerassimos Barbatis and Achilles Tertikas
3 Sharp singular Trudinger-Moser-Adams type inequalities with exact growth. Nguyen Lam and Guozhen Lu. 4 A Quantitative Lusin Theorem for Functions in BV. András Telcs and Vincenzo Vespri
5 X-Elliptic Harmonic Maps. Sorin Dragomir
6 Sum operators and Fefferman - Phong inequalities. Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni
7 Lp-parabolic regularity and non-degenerate Ornstein-Uhlenbeck type Operators. Enrico Priola
8 Local solvability of nonsmooth Hörmander’s operators. Marco Bramanti
9 Multiple solutions for an eigenvalue problem involving non–local elliptic p–Laplacian operators. Patrizia Pucci and Sara Saldi
10 Uniqueness of solutions of a class of quasilinear subelliptic equations. Lorenzo D’Ambrosio and Enzo Mitidieri
11 Liouville type theorems for non-linear differential inequalities on Carnot groups. Luca Brandolini and Marco Magliaro
12 Modica type gradient estimates for reaction-diffusion equations. Agnid Banerjee and Nicola Garofalo
13 A few recent results on fully nonlinear pde’s. Italo Capuzzo Dolcetta
14 Hölder regularity of the gradient for solutions of fully nonlinear equations with sub linear first order term. Isabeau Birindelli and Francoise Demengel
15 The Reflector Problem and the inverse square law. Cristian E. Gutiérrez and Ahmad Sabra
16 Gagliardo-Nirenberg inequalities for horizontal vector fields in the Engel group and in the 7-dimensional quaternionic Heisenberg group. Annalisa Baldi, Bruno Franchi and Francesca Tripaldi
17 Regularity of the free boundary in problems with distributed sources. Daniela De Silva, Fausto Ferrari, Sandro Salsa
18 The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE. Andrea Bonfiglioli, Giovanna Citti, Giovanni Cupini, Maria Manfredini, Annamaria Montanari, Daniele Morbidelli, Andrea Pascucci, Sergio Polidoro, Francesco Uguzzoni
1 On Friedrichs commutators lemma for Hardy spaces and applications. Jorge Hounie
2 On the Hardy constant of some non-convex planar domains. Gerassimos Barbatis and Achilles Tertikas
3 Sharp singular Trudinger-Moser-Adams type inequalities with exact growth. Nguyen Lam and Guozhen Lu. 4 A Quantitative Lusin Theorem for Functions in BV. András Telcs and Vincenzo Vespri
by Hans G. Feichtinger, Bernard Helffer, Michael P. Lamoureux, Nicolas Lerner, Joachim Toft ; edited by J. -M. Morel, F. Takens, B. Teissier, Luigi Rodino, M. W. Wong
出版情報:
Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008
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