APPLICATIONS OF P-ADIC GENERALIZED FUNCTIONS AND APPROXIMATIONS BY A SYSTEM OF P-ADIC TRANSLATIONS OF A FUNCTION

S. S. Volosivets

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APPLICATIONS OF P-ADIC GENERALIZED FUNCTIONS AND APPROXIMATIONS BY A SYSTEM OF P-ADIC TRANSLATIONS OF A FUNCTION

机译：函数的P-ADIC翻译系统在P-ADIC广义函数中的应用和逼近

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摘要

Under some conditions we prove that the convergence of a sequence of functions in the space of P-adic generalized functions is equivalent to its convergence in the space of locally integrable functions. Some analogs are established of the Wiener tauberian theorem and the Wiener theorem on denseness of translations for P-adic convolutions and translations.

机译：在某些条件下，我们证明了P-adic广义函数空间中的一系列函数的收敛性等同于局部可积函数空间中的一系列函数的收敛性。建立了针对P-adic卷积和平移的平移密度的Wiener陶伯定理和Wiener定理的一些类似物。

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来源
《Siberian Mathematical Journal》 |2009年第1期|共13页
作者
S. S. Volosivets;
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原文格式 PDF
正文语种 eng
中图分类 510LB010;
关键词
P-adic generalized function; Lp; multiplicative Fourier transform; Lebesgue points of order p; Wiener tauberian theorem; Wiener theorem on denseness of translations;

机译：P-adic广义函数;Lp;可乘傅立叶变换;Lebesgue阶p;Wiener陶伯定理;关于翻译密度的Wiener定理;

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专利

1. APPLICATIONS OF P-ADIC GENERALIZED FUNCTIONS AND APPROXIMATIONS BY A SYSTEM OF P-ADIC TRANSLATIONS OF A FUNCTION [J] . S. S. Volosivets Siberian Mathematical Journal . 2009,第1期

机译：函数的P-ADIC翻译系统在P-ADIC广义函数中的应用和逼近
2. p-Adic interpolation and approximation of a continuous function by linear combinations of shifts of p-adic valuations [J] . Khrennikov A., Radyna A. Journal of Approximation Theory . 2003,第1期

机译：p-adic内插和通过p-adic估值的偏移的线性组合来逼近连续函数
3. p-Adic measures associated with zeta values and p-adic log multiple gamma functions [J] . Kashio Tomokazu International Journal of Number Theory . 2019,第5期

机译：与zeta值和p-adic对数伽玛函数相关的p-Adic度量
4. 3 p-adic L-functions and Euler systems: a tale in two trilogies [C] . Massimo Bertolini, Francesc Castella, Henri Darmon, Symposium on Galois Representations and Automorphic Forms . 2014

机译：3 P-ADIC L函数和欧拉系统：两个三部曲中的故事
5. A New p-Adic Maass-Shimura Operator and Supersingular Rankin-Selberg p-Adic L-Functions [D] . Kriz, Daniel J. 2018

机译：一个新的p-Adic Maass-Shimura算子和超奇异的Rankin-Selberg p-Adic L-函数
6. Colloquium Paper: p-adic L functions and trivial zeroes [O] . Bernadette Perrin-Riou 1997

机译：座谈会论文：p-adic L函数和平凡零
7. On a q-analogue of the p-adic generalized twisted L-functions and p-adic q-integrals [O] . Lee-chae Jang, Tae-gyun Kim, Young-chang Ri, 2012

机译：关于p-adic广义扭曲L函数和p-adic q-积分的q模拟

APPLICATIONS OF P-ADIC GENERALIZED FUNCTIONS AND APPROXIMATIONS BY A SYSTEM OF P-ADIC TRANSLATIONS OF A FUNCTION

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