A comparison principle for convolution measures with applications
| Autor: | René Quilodrán, Diogo Oliveira e Silva |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pointwise
Paraboloid Computer Science::Information Retrieval General Mathematics 010102 general mathematics Mathematical analysis Parabola Regular polygon 01 natural sciences Measure (mathematics) Projection (linear algebra) Convolution symbols.namesake Fourier transform Mathematics - Classical Analysis and ODEs 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Mathematics |
| Popis: | We establish the general form of a geometric comparison principle for $n$-fold convolutions of certain singular measures in $\mathbb{R}^d$ which holds for arbitrary $n$ and $d$. This translates into a pointwise inequality between the convolutions of projection measure on the paraboloid and a perturbation thereof, and we use it to establish a new sharp Fourier extension inequality on a general convex perturbation of a parabola. Further applications of the comparison principle to sharp Fourier restriction theory are discussed in a companion paper. Comment: 17 pages, v2: updated reference to companion paper |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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