Functional Analysis, Harmonic Analysis, and Image Processing A Collection of Papers in Honor of Björn Jawerth
This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course i...
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| Main Authors: | , |
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| Format: | eBook Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2017
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| Edition: | 1 |
| Series: | Contemporary Mathematics |
| Subjects: | |
| ISBN: | 9781470428365, 1470428369 |
| ISSN: | 0271-4132, 1098-3627 |
| Online Access: | Get full text |
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Table of Contents:
- Björn David Jawerth (1952–2013) -- Jawerth–Milman extrapolation theory: Some recent developments with applications -- Uncertainty principles and weighted norm inequalities -- The discrete Calderón reproducing formula of Frazier and Jawerth -- A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels -- An approximation problem in multiplicatively invariant spaces -- Discrete decomposition of homogeneous mixed-norm Besov spaces -- From Frazier-Jawerth characterizations of Besov spaces to wavelets and decomposition spaces -- Traces and extensions of weighted Sobolev and potential spaces -- Compact embeddings of weighted smoothness spaces of Morrey type: An example -- Tracking the structural deformation of a sheared biopolymer network -- Extrapolation, a technique to estimate -- On a dual property of the maximal operator on weighted variable <inline-formula content-type="math/mathml"> L p L^p </inline-formula> spaces -- Is the Dirichlet space a quotient of <inline-formula content-type="math/mathml"> D A n DA_{n} </inline-formula>? -- Characterizations of the Hardy space <inline-formula content-type="math/mathml"> H 1 ( R ) H^1(\mathbb {R}) </inline-formula> and BMO<inline-formula content-type="math/mathml"> ( R ) (\mathbb {R}) </inline-formula> -- Four proofs of cocompactness for Sobolev embeddings -- Tempered homogeneous function spaces, II -- Isotropic and dominating mixed Besov spaces: A comparison -- An iteratively reweighted least squares algorithm for sparse regularization
- References -- Is the Dirichlet space a quotient of _{ }? -- 1. Statement of the Result -- 2. Background -- 3. A Reformulation Using the Metric -- 4. Preliminary Estimates -- 5. Proof of the Theorem -- 6. Final Remarks -- 7. Afterword -- References -- Characterizations of the Hardy space ¹(ℝ) and BMO(ℝ) -- 1. Introduction -- 2. The Hardy Space ¹(\R) -- 3. Characterizations of BMO(\R) -- References -- Four proofs of cocompactness for Sobolev embeddings -- 1. Introduction -- 2. Capacity-type argument -- 3. Proof by partition of domain and range -- 4. Proof by the wavelet decomposition -- 5. Proof via the Littlewood-Paley decomposition -- References -- Tempered homogeneous function spaces, II -- 1. Introduction and motivation -- 2. Definitions and basic assertions -- 2.1. Preliminaries and inhomogeneous spaces -- 2.2. Spaces with negative smoothness -- 2.3. Spaces in the distinguished strip -- 3. Properties -- 3.1. Embeddings -- 3.2. Global inequalities for heat equations -- 3.3. Hardy inequalities -- 3.4. Multiplication algebras -- 3.5. Examples I: Riesz kernels -- 3.6. Examples II: Mixed Riesz kernels -- References -- Isotropic and dominating mixed Besov spaces: A comparison -- 1. Introduction -- 2. Besov spaces of isotropic and dominating mixed smoothness -- 3. The main results -- 4. Proofs -- Acknowledgement -- References -- An iteratively reweighted least squares algorithm for sparse regularization -- 1. Introduction -- 2. Constructions -- 3. Analysis of the IRLS algorithm -- 4. Numerics -- 5. Conclusions -- References -- Back Cover
- Discrete decomposition of homogeneous mixed-norm Besov spaces -- 1. Introduction -- 2. Preliminaries -- 3. Homogeneous mixed-norm Besov spaces -- 4. The -transform -- 5. Inhomogeneous mixed-norm Besov spaces -- 6. Appendix -- References -- From Frazier-Jawerth characterizations of Besov spaces to wavelets and decomposition spaces -- 1. The Frazier-Jawerth Atomic Characterizations -- 2. Coorbit Theory -- 3. Decomposition Spaces -- 4. Abstract and Concrete Wavelet Theory -- Acknowledgments -- References -- Traces and extensions of weighted Sobolev and potential spaces -- 1. Introduction -- 2. Decomposition of Weighted Function Spaces -- 3. Traces and Extensions -- References -- Compact embeddings of weighted smoothness spaces of Morrey type: An example -- Introduction -- 1. Function spaces -- 2. Continuous embeddings -- 3. Compact embeddings of weighted spaces: a model case -- References -- Tracking the structural deformation of a sheared biopolymer network -- Introduction -- The Method -- Overview of the Tracking Algorithm -- 1. Initial Processing: Network Extraction -- 2. Selection of features and search regions -- 3. Finding the displacement of a feature region within the corresponding search region -- Application of algorithm to a fibrin network undergoing shear -- 4. Details of data acquisition and application of the tracking algorithm -- 5. Discussion -- 6. Material and Methods -- 7. Acknowledgements -- References -- Extrapolation, a technique to estimate -- 1. Introduction -- 2. Background -- 3. The main results -- 4. Application. Extending holomorphic sections -- References -- On a dual property of the maximal operator on weighted variable ^{ } spaces -- 1. Introduction -- 2. Preliminaries -- 3. Maximal operator on associate spaces -- 4. Proof of Theorem 1.1 -- 5. Proof of Lemma 4.1 -- 6. Concluding remarks and open questions
- Cover -- Title page -- Contents -- Preface -- Björn David Jawerth (1952-2013) -- Jawerth-Milman extrapolation theory: Some recent developments with applications -- 1. Introduction and preliminaries -- 2. Interplay between interpolation and extrapolation -- 3. Stability of weighted Δ-functors on _{ , }-spaces -- 4. Strong extrapolation spaces -- 5. Probabilistic moment problem -- 6. Extrapolation of operators with a quasi-Banach target space -- References -- Uncertainty principles and weighted norm inequalities -- 1. Introduction -- 2. The classical uncertainty principle inequality for ²(ℝ^{ }) -- 3. Hardy type inequalities -- 4. Weighted Fourier transform norm inequalities -- 5. Uncertainty principle inequalities -- 6. An uncertainty principle inequality for Hilbert spaces -- 7. Epilogue -- References -- The discrete Calderón reproducing formula of Frazier and Jawerth -- 1. The Continuous Calderón Reproducing Formula -- 2. The Discrete Calderón Reproducing Formula -- 3. Characterization of function spaces, atoms, and molecules -- 4. Almost orthogonality and almost diagonal operators -- 5. Concluding remarks -- Acknowledgement -- References -- A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels -- 1. Introduction and statements of main results -- 2. Preliminary Results -- 3. Pointwise Definition of the Convolution -- 4. Maximal Inequalities -- 5. Proof of Characterisation Theorems -- 6. Appendix -- References -- An approximation problem in multiplicatively invariant spaces -- 1. Introduction -- 2. Preliminaries -- 3. Decomposable MI spaces in ²(Ω,ℋ) -- 4. Approximation problems -- 5. Application to SI spaces in LCA groups -- 6. Totally decomposable MI spaces and translation-invariant spaces -- 7. Acknowledgments -- Appendix A. -- References