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Тауберовы оценки класса для векторнозначных обобщенных функций

(2019) MATEMATIČESKIJ SBORNIK. 210(2). p.115-142
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Abstract
Изучаются тауберовы свойства регуляризующих преобразований век- торнозначных обобщенных функций медленного роста, а именно преоб- разований вида M_φf (x, y) = (f ∗ φ_y )(x), где ядро φ является основной функцией и φ_y(·) = y^{−n}φ(·/y). Исследуются условия, при которых обоб- щенная функция, априори принимающая значения в локально выпуклом пространстве, в действительности принимает значения в более узком, ба- наховом пространстве. Цель настоящей статьи состоит в характериза- ции пространств обобщенных функций медленного роста со значениями в банаховом пространстве в терминах так называемых оценок класса для преобразования M_φf (x, y). Результаты работы обобщают и уточняют ра- нее полученные тауберовы теоремы Ю. Н. Дрожжинова и Б. И. Завьялова. Особое внимание уделяется нахождению оптимального класса ядер φ, для которого справедливы эти тауберовы результаты.
Keywords
regularizing transforms, class estimates, Tauberian theorems, vector-valued distributions, generalized functions, wavelet transform

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Chicago
Pilipovic, Stevan, and Jasson Vindas Diaz. 2019. “Тауберовы Оценки Класса Для Векторнозначных Обобщенных Функций.” Matematičeskij Sbornik 210 (2): 115–142.
APA
Pilipovic, S., & Vindas Diaz, J. (2019). Тауберовы оценки класса для векторнозначных обобщенных функций. MATEMATIČESKIJ SBORNIK, 210(2), 115–142.
Vancouver
1.
Pilipovic S, Vindas Diaz J. Тауберовы оценки класса для векторнозначных обобщенных функций. MATEMATIČESKIJ SBORNIK. 2019;210(2):115–42.
MLA
Pilipovic, Stevan, and Jasson Vindas Diaz. “Тауберовы Оценки Класса Для Векторнозначных Обобщенных Функций.” MATEMATIČESKIJ SBORNIK 210.2 (2019): 115–142. Print.
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\unmatched{0440}\unmatched{0430}\unmatched{0437}\unmatched{043e}\unmatched{0432}\unmatched{0430}\unmatched{043d}\unmatched{0438}\unmatched{0438}\unmatched{0306} \unmatched{0432}\unmatched{0438}\unmatched{0434}\unmatched{0430} M\_\ensuremath{\phi}f (x, y) = (f \ensuremath{\ast} \ensuremath{\phi}\_y )(x), \unmatched{0433}\unmatched{0434}\unmatched{0435} \unmatched{044f}\unmatched{0434}\unmatched{0440}\unmatched{043e} \ensuremath{\phi} \unmatched{044f}\unmatched{0432}\unmatched{043b}\unmatched{044f}\unmatched{0435}\unmatched{0442}\unmatched{0441}\unmatched{044f} \unmatched{043e}\unmatched{0441}\unmatched{043d}\unmatched{043e}\unmatched{0432}\unmatched{043d}\unmatched{043e}\unmatched{0438}\unmatched{0306} \unmatched{0444}\unmatched{0443}\unmatched{043d}\unmatched{043a}\unmatched{0446}\unmatched{0438}\unmatched{0435}\unmatched{0438}\unmatched{0306} \unmatched{0438} \ensuremath{\phi}\_y({\textperiodcentered}) = y\^{ }\{\ensuremath{-}n\}\ensuremath{\phi}({\textperiodcentered}/y). 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\unmatched{0431}\unmatched{0430}\unmatched{043d}\unmatched{0430}\unmatched{0445}\unmatched{043e}\unmatched{0432}\unmatched{043e}\unmatched{043c} \unmatched{043f}\unmatched{0440}\unmatched{043e}\unmatched{0441}\unmatched{0442}\unmatched{0440}\unmatched{0430}\unmatched{043d}\unmatched{0441}\unmatched{0442}\unmatched{0432}\unmatched{0435} \unmatched{0432} \unmatched{0442}\unmatched{0435}\unmatched{0440}\unmatched{043c}\unmatched{0438}\unmatched{043d}\unmatched{0430}\unmatched{0445} \unmatched{0442}\unmatched{0430}\unmatched{043a} \unmatched{043d}\unmatched{0430}\unmatched{0437}\unmatched{044b}\unmatched{0432}\unmatched{0430}\unmatched{0435}\unmatched{043c}\unmatched{044b}\unmatched{0445} \unmatched{043e}\unmatched{0446}\unmatched{0435}\unmatched{043d}\unmatched{043e}\unmatched{043a} \unmatched{043a}\unmatched{043b}\unmatched{0430}\unmatched{0441}\unmatched{0441}\unmatched{0430} \unmatched{0434}\unmatched{043b}\unmatched{044f} \unmatched{043f}\unmatched{0440}\unmatched{0435}\unmatched{043e}\unmatched{0431}\unmatched{0440}\unmatched{0430}\unmatched{0437}\unmatched{043e}\unmatched{0432}\unmatched{0430}\unmatched{043d}\unmatched{0438}\unmatched{044f} M\_\ensuremath{\phi}f (x, y). \unmatched{0420}\unmatched{0435}\unmatched{0437}\unmatched{0443}\unmatched{043b}\unmatched{044c}\unmatched{0442}\unmatched{0430}\unmatched{0442}\unmatched{044b} \unmatched{0440}\unmatched{0430}\unmatched{0431}\unmatched{043e}\unmatched{0442}\unmatched{044b} \unmatched{043e}\unmatched{0431}\unmatched{043e}\unmatched{0431}\unmatched{0449}\unmatched{0430}\unmatched{044e}\unmatched{0442} \unmatched{0438} \unmatched{0443}\unmatched{0442}\unmatched{043e}\unmatched{0447}\unmatched{043d}\unmatched{044f}\unmatched{044e}\unmatched{0442} \unmatched{0440}\unmatched{0430}- \unmatched{043d}\unmatched{0435}\unmatched{0435} \unmatched{043f}\unmatched{043e}\unmatched{043b}\unmatched{0443}\unmatched{0447}\unmatched{0435}\unmatched{043d}\unmatched{043d}\unmatched{044b}\unmatched{0435} \unmatched{0442}\unmatched{0430}\unmatched{0443}\unmatched{0431}\unmatched{0435}\unmatched{0440}\unmatched{043e}\unmatched{0432}\unmatched{044b} \unmatched{0442}\unmatched{0435}\unmatched{043e}\unmatched{0440}\unmatched{0435}\unmatched{043c}\unmatched{044b} \unmatched{042e}. \unmatched{041d}. \unmatched{0414}\unmatched{0440}\unmatched{043e}\unmatched{0436}\unmatched{0436}\unmatched{0438}\unmatched{043d}\unmatched{043e}\unmatched{0432}\unmatched{0430} \unmatched{0438} \unmatched{0411}. \unmatched{0418}. \unmatched{0417}\unmatched{0430}\unmatched{0432}\unmatched{044c}\unmatched{044f}\unmatched{043b}\unmatched{043e}\unmatched{0432}\unmatched{0430}. \unmatched{041e}\unmatched{0441}\unmatched{043e}\unmatched{0431}\unmatched{043e}\unmatched{0435} \unmatched{0432}\unmatched{043d}\unmatched{0438}\unmatched{043c}\unmatched{0430}\unmatched{043d}\unmatched{0438}\unmatched{0435} \unmatched{0443}\unmatched{0434}\unmatched{0435}\unmatched{043b}\unmatched{044f}\unmatched{0435}\unmatched{0442}\unmatched{0441}\unmatched{044f} \unmatched{043d}\unmatched{0430}\unmatched{0445}\unmatched{043e}\unmatched{0436}\unmatched{0434}\unmatched{0435}\unmatched{043d}\unmatched{0438}\unmatched{044e} \unmatched{043e}\unmatched{043f}\unmatched{0442}\unmatched{0438}\unmatched{043c}\unmatched{0430}\unmatched{043b}\unmatched{044c}\unmatched{043d}\unmatched{043e}\unmatched{0433}\unmatched{043e} \unmatched{043a}\unmatched{043b}\unmatched{0430}\unmatched{0441}\unmatched{0441}\unmatched{0430} \unmatched{044f}\unmatched{0434}\unmatched{0435}\unmatched{0440} \ensuremath{\phi}, \unmatched{0434}\unmatched{043b}\unmatched{044f} \unmatched{043a}\unmatched{043e}\unmatched{0442}\unmatched{043e}\unmatched{0440}\unmatched{043e}\unmatched{0433}\unmatched{043e} \unmatched{0441}\unmatched{043f}\unmatched{0440}\unmatched{0430}\unmatched{0432}\unmatched{0435}\unmatched{0434}\unmatched{043b}\unmatched{0438}\unmatched{0432}\unmatched{044b} \unmatched{044d}\unmatched{0442}\unmatched{0438} \unmatched{0442}\unmatched{0430}\unmatched{0443}\unmatched{0431}\unmatched{0435}\unmatched{0440}\unmatched{043e}\unmatched{0432}\unmatched{044b} \unmatched{0440}\unmatched{0435}\unmatched{0437}\unmatched{0443}\unmatched{043b}\unmatched{044c}\unmatched{0442}\unmatched{0430}\unmatched{0442}\unmatched{044b}.
},
  author       = {Pilipovic, Stevan and Vindas Diaz, Jasson},
  issn         = {0368-8666},
  journal      = {MATEMATI\v{C}ESKIJ SBORNIK},
  language     = {rus},
  number       = {2},
  pages        = {115--142},
  title        = {\unmatched{0422}\unmatched{0430}\unmatched{0443}\unmatched{0431}\unmatched{0435}\unmatched{0440}\unmatched{043e}\unmatched{0432}\unmatched{044b} \unmatched{043e}\unmatched{0446}\unmatched{0435}\unmatched{043d}\unmatched{043a}\unmatched{0438} \unmatched{043a}\unmatched{043b}\unmatched{0430}\unmatched{0441}\unmatched{0441}\unmatched{0430} \unmatched{0434}\unmatched{043b}\unmatched{044f} \unmatched{0432}\unmatched{0435}\unmatched{043a}\unmatched{0442}\unmatched{043e}\unmatched{0440}\unmatched{043d}\unmatched{043e}\unmatched{0437}\unmatched{043d}\unmatched{0430}\unmatched{0447}\unmatched{043d}\unmatched{044b}\unmatched{0445} \unmatched{043e}\unmatched{0431}\unmatched{043e}\unmatched{0431}\unmatched{0449}\unmatched{0435}\unmatched{043d}\unmatched{043d}\unmatched{044b}\unmatched{0445} \unmatched{0444}\unmatched{0443}\unmatched{043d}\unmatched{043a}\unmatched{0446}\unmatched{0438}\unmatched{0439}},
  url          = {http://dx.doi.org/10.4213/sm9061},
  volume       = {210},
  year         = {2019},
}

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