Radon transforms, geometry, and wavelets : AMS Special Session, January 7-8, 2007, New Orleans, Louisiana : Workshop, January 4-5, 2007, Baton Rouge, Louisiana / Gestur Ólafsson [and six others], editors.

Format:

Book

Conference/Event

Contributor:

Ólafsson, Gestur, editor.

Conference Name:

AMS Special Session on Radon Transforms, Convex Geometry, and Geometric Analysis (2007 : New Orleans, La.), issuing body.

AMS Special Session on Frames and Wavelets in Harmonic Analysis, Geometry, and Applications (2007 : New Orleans, La.), issuing body.

Workshop on Harmonic Analysis and Applications (2007 : Baton Rouge, La.), issuing body.

Series:

Contemporary mathematics (American Mathematical Society) ; v. 464.

Contemporary mathematics, 0271-4132 ; 464

Language:

English

Subjects (All):

Integral geometry--Congresses.

Integral geometry.

Integral transforms--Congresses.

Integral transforms.

Harmonic analysis--Congresses.

Harmonic analysis.

Physical Description:

1 online resource (282 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2008]

Language Note:

English

Summary:

This volume is based on two special sessions held at the AMS Annual Meeting in New Orleans in January 2007, and a satellite workshop held in Baton Rouge on January 4-5, 2007. It consists of invited expositions that together represent a broad spectrum of fields, stressing surprising interactions and connections between areas that are normally thought of as disparate. The main topics are geometry and integral transforms. On the one side are harmonic analysis, symmetric spaces, representation theory (the groups include continuous and discrete, finite and infinite, compact and non-compact), operator theory, PDE, and mathematical probability. Moving in the applied direction we encounter wavelets, fractals, and engineering topics such as frames and signal and image processing.The subjects covered in this book form a unified whole, and they stand at the crossroads of pure and applied mathematics. The articles cover a broad range in harmonic analysis, with the main themes related to integral geometry, the Radon transform, wavelets and frame theory. These themes can loosely be grouped together as follows:Frame Theory and ApplicationsHarmonic Analysis and Function SpacesHarmonic Analysis and Number TheoryIntegral Geometry and Radon TransformsMultiresolution Analysis, Wavelets, and Applications.

Contents:

""Contents""; ""Preface""; ""Combined List of Speakers and Titles of Their Talks""; ""Composite Wavelet Transforms: Applications and Perspectives""; ""1. Introduction.""; ""2. Composite wavelet transforms for dilated kernels.""; ""3. Wavelet transforms associated to one-parametric semigroups and inversion of potentials.""; ""4. Wavelet transforms with the generalized translation operator.""; ""5. Beta-semigroups.""; ""6. Parabolic wavelet transforms.""; ""7. Some applications to inversion of the k-plane Radon transform.""; ""8. Higher-rank composite wavelet transforms and open problems.""

""References""""Complex Sigma-Delta Quantization Algorithms for Finite Frames""; ""Decomposition and Admissibility for the Quasiregular Representation for Generalized Oscillator Groups""; ""Fourier Series on Fractals: A Parallel with Wavelet Theory""; ""1. Introduction""; ""1.1. Complex systems""; ""2. Multiresolution wavelets and Iterated Function Systems""; ""2.1. The attractor""; ""2.2. Multiresolutions""; ""2.3. The scaling equation, the invariance equation""; ""2.4. Orthogonality of the translates of the scaling function; orthogonality of the exponentials""

""2.5. The quadrature mirror filter condition and Hadamard triples""""2.6. Lawton's theorem and transfer operators""; ""2.7. Cohen's orthogonality condition and the Laba-Wang theorem""; ""2.8. Super-wavelets and the completion of Î?0""; ""3. Open problems""; ""4. Appendix, with some of Jorgensen's recollections of conversations with Irving Segal, Marshall Stone, Bent Fuglede, and David Shale.""; ""References""; ""A Computational Complexity Paradigm for Tomography""; ""Invariant Differential Operators on Matrix Motion Groups and Applications to the Matrix Radon Transform""

""Helgason's Support Theorem and Spherical Radon Transforms""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

9780821881439

0821881434

9780821843277

0821843273

OCLC:

922981024