Exponentially sparse representations of Fourier integral operators
| Autor: | Luigi Rodino, Elena Cordero, Fabio Nicola |
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| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
General Mathematics Microlocal analysis Canonical transformation Schrödinger equations Fourier integral operator Mathematics - Analysis of PDEs sparse representations FOS: Mathematics Fourier integral operators Mathematics Quadratic growth Gelfand-Shilov spaces Short-time Fourier transform Gabor frames Mathematical analysis Operator theory Gelfand Shilov spaces Functional Analysis (math.FA) short-time Fourier transform Exponential function Mathematics - Functional Analysis 35S30 35A20 42C15 Analysis of PDEs (math.AP) Counterexample |
| Zdroj: | Revista Matemática Iberoamericana. 31:461-476 |
| ISSN: | 0213-2230 |
| Popis: | We investigate the sparsity of the Gabor-matrix representation of Fourier integral operators with a phase having quadratic growth. It is known that such an infinite matrix is sparse and well organized, being in fact concentrated along the graph of the corresponding canonical transformation. Here we show that, if the phase and symbol have a regularity of Gevrey type of order $s>1$ or analytic ($s=1$), the above decay is in fact sub-exponential or exponential, respectively. We also show by a counterexample that ultra-analytic regularity ($s 15 pages |
| Databáze: | OpenAIRE |
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