Items related to The Uncertainty Principle in Harmonic Analysis
Synopsis
One. The Uncertainty Principle Without Complex Variables.- 1. Functions and Charges with Semibounded Spectra.- §1. The Uncertainty Principle for Charges with Semibounded Spectra. The F. and M. Riesz Theorem.- §2. Sharpness of the F. and M. Riesz Theorem. The Rudin-Carleson Theorem.- §3. A Quantitative Refinement of the F. and M. Riesz Theorem.- §4. The De Leeuw-Katznelson Theorem.- §5. One More Quantitative Refinement of the F. and M. Riesz Theorem.- §6. Some Multidimensional Generalizations and Analogs of the F. and M. Riesz Theorem. The Approach of Aleksandrov and Shapiro.- §7. Perturbed Plus-Charges.- Notes.- 2. Some Topics Related to the Harmonic Analysis of Charges.- §1. r-Charges.- §2. Cantor Measures.- §3. The Riesz Products.- §4. The Ivashev-Musatov Theorem.- §5. The Lemma on the Optimal Régime. The Role of Regularity Properties of the Majorant in the Ivashev-Musatov Theorem.- §6. Deep Zeros and Sparse Spectra. A "Real" Proof of the Mandelbrojt Theorem.- Notes.- 3. Hilbert Space Methods.- §1. Mutually Annihilating Pairs of Subspaces.- §2. Annihilation of Supports and Spectra of Finite Volume. The Amrein-Berthier and Slepian-Pollak Theorems.- §3. Functions with Sparse Spectra. The Mikheyev Theorem.- §4. Supports Strongly Annihilating any Bounded Spectrum. The Logvinenko-Sereda Theorem.- Notes.- Two. Complex Methods.- 1. The Uncertainty Principle from the Complex Point of View. First Examples.- §1. Introductory Remarks.- §2. The Limit Speed of Decay of the Fourier Transform of a Rapidly Decreasing Function. The Dzhrbashyan Theorem.- §3. A Complex Proof of the Mandelbrojt Theorem.- §4. The UP for Plus-Functions from a New Point of View.- §5. Hardy Classes in the Upper Half-Plane.- §6. The Lindelöf Theorem. Entire Functions of the Cartwright Class.- Notes.- 2. The Logarithmic Integral Diverges.- §1. Divergence of a Logarithmic Integral and Some Forms of the UP for Functions and Charges with Rapidly Decreasing Amplitudes. The Beurling Theorem.- §2. Charges with a Spectral Gap.- §3. One-Sided Decrease of Amplitudes. The Volberg Theorems.- §4. One-Sided Decrease and One-sided Growth of Amplitudes. The Borichev Approach.- Notes.- 3. The Logarithmic Integral Converges.- §1. Outer Functions. Sharpness of Some Forms of the UP.- §2. The Khinchin-Ostrowski Theorem.- §3. Unilateral Decrease of Amplitudes and the Size of Support. The Hruscev Theorem.- §4. The Hruscev Theorem: the End of the Proof.- §5. The First Beurling-Malliavin Theorem.- §6. Functions with Finite Dirichlet Integral in a Half-Plane and Their Boundary Values.- §7. Logarithmic Potential and Distributions of Finite Energy.- §8. The Spectral Gap Problem Revisited.- §9. The Sapogov Problem: Characteristic Functions with a Spectral Gap.- Notes.- 4. Missing Frequencies and the Diameter of the Support. The Second Beurling-Malliavin Theorem and the Fabry Theorem.- §1. Statement of the Problem. The Diameter of a Divisor.- §2. Systems of Long and Short Intervals. A Covering Lemma.- §3. Three Definitions of the Integral Density of a Measure.- §4. The Estimate ?3(?) ? R(?).- §5. The Estimate ?1(?) ? R(?).- §6. The Fabry Theorem: Technical Preliminaries.- §7. The Fabry and Carlson-Landau Theorems. The First Proof.- §8. Sharpness of the Carlson-Landau Theorem.- §9. The Fabry Theorem. The Second Proof.- §10. The Fabry Theorem. The Third Proof.- §11. The Amrein-Berthier Theorem Revisited. The Nazarov Approach.- §12. Concluding Remarks. The Fabry Phenomenon.- Notes.- 5. Local and Non-local Convolution Operators.- §1. Symbols of Local Operators.- §2. Semirational Symbols and Complete Antilocality.- §3. The Cauchy Problem for the Laplace Equation.- §4. Complete Antilocality of One-Dimensional M. Riesz Potentials.- Notes.- References.- Author Index.
"synopsis" may belong to another edition of this title.
(No Available Copies)
Search Books: Create a WantCan't find the book you're looking for? We'll keep searching for you. If one of our booksellers adds it to AbeBooks, we'll let you know!
Create a Want
