Some estimates of special classes of integrals

We study the integrals fb a f(t) exp(i| ln rt|σ) dt and obtain asymptotic formula for these functions of non‐regular growth. This is a peculiar kind of the theory asymptotic expansions. In particular, we get asymptotic formulae for different entire functions of non‐regular growth. Asymptotic formul...

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Main Author: T. I. Malyutina
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2000-12-01
Series:Mathematical Modelling and Analysis
Subjects:
-
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/9951
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spelling doaj-171ab9d1525243d3bd5fba6396877dd62021-07-02T13:54:50ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102000-12-015110.3846/13926292.2000.9637135Some estimates of special classes of integralsT. I. Malyutina0Ukrainian Academy of Banking , PetroPavlovska Str. 56, Sumy, 244030, Ukraine We study the integrals fb a f(t) exp(i| ln rt|σ) dt and obtain asymptotic formula for these functions of non‐regular growth. This is a peculiar kind of the theory asymptotic expansions. In particular, we get asymptotic formulae for different entire functions of non‐regular growth. Asymptotic formulas for Levin‐Pfluger entire functions of completely regular growth are well‐known [1]. Our formulas allow to find limiting Azarin's [2] sets for some subharmonic functions. The kernel exp(i| ln rt|σ) contains arbitrary parameter σ > 0. The integrals for σ ∈(0, 1), σ = 1, σ > 1 essentially differ. Our arguments can apply to more general kernels. We give a new variant of the classic lemma of Riemann and Lebesgue from the theory of the transformation of Fourier. Specialiųjų integralų klasių įverčiai Santrauka Darbe nagrinejami integralai fb a f(t) exp(i| ln r|σ) dt ir tiriamos šiu nereguliaraus augimo greičiu funkciju asimptotines formules. Gautos naujos asimptotines formules, leidžiančios rasti Azarino aibes kai kurioms subharmoninems funkcijoms. Branduolys exp(i| ln rt|σ) priklauso nuo vieno parametro σ > 0. Trys atvejai, kai 0 < σ < 1, σ = 1 ir σ > 0, yra esminiai skirtingi. Darbo metodika gali būti naudojama ir bendresniems branduoliu atvejams. Irodytas naujas Rimano ir Lebego lemos varijantas, kuris naudojamas Furje transformacijos teorijoje. First Published Online: 14 Oct 2010 https://journals.vgtu.lt/index.php/MMA/article/view/9951-
collection DOAJ
language English
format Article
sources DOAJ
author T. I. Malyutina
spellingShingle T. I. Malyutina
Some estimates of special classes of integrals
Mathematical Modelling and Analysis
-
author_facet T. I. Malyutina
author_sort T. I. Malyutina
title Some estimates of special classes of integrals
title_short Some estimates of special classes of integrals
title_full Some estimates of special classes of integrals
title_fullStr Some estimates of special classes of integrals
title_full_unstemmed Some estimates of special classes of integrals
title_sort some estimates of special classes of integrals
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2000-12-01
description We study the integrals fb a f(t) exp(i| ln rt|σ) dt and obtain asymptotic formula for these functions of non‐regular growth. This is a peculiar kind of the theory asymptotic expansions. In particular, we get asymptotic formulae for different entire functions of non‐regular growth. Asymptotic formulas for Levin‐Pfluger entire functions of completely regular growth are well‐known [1]. Our formulas allow to find limiting Azarin's [2] sets for some subharmonic functions. The kernel exp(i| ln rt|σ) contains arbitrary parameter σ > 0. The integrals for σ ∈(0, 1), σ = 1, σ > 1 essentially differ. Our arguments can apply to more general kernels. We give a new variant of the classic lemma of Riemann and Lebesgue from the theory of the transformation of Fourier. Specialiųjų integralų klasių įverčiai Santrauka Darbe nagrinejami integralai fb a f(t) exp(i| ln r|σ) dt ir tiriamos šiu nereguliaraus augimo greičiu funkciju asimptotines formules. Gautos naujos asimptotines formules, leidžiančios rasti Azarino aibes kai kurioms subharmoninems funkcijoms. Branduolys exp(i| ln rt|σ) priklauso nuo vieno parametro σ > 0. Trys atvejai, kai 0 < σ < 1, σ = 1 ir σ > 0, yra esminiai skirtingi. Darbo metodika gali būti naudojama ir bendresniems branduoliu atvejams. Irodytas naujas Rimano ir Lebego lemos varijantas, kuris naudojamas Furje transformacijos teorijoje. First Published Online: 14 Oct 2010
topic -
url https://journals.vgtu.lt/index.php/MMA/article/view/9951
work_keys_str_mv AT timalyutina someestimatesofspecialclassesofintegrals
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