scholarly journals On absolute summability of Fourier integrals with multipliers

1987 ◽  
pp. 78
Author(s):  
L.G. Bojtsun ◽  
A.I. Khaliuzova
Keyword(s):  
Fourier Integral ◽  
Functional Method ◽  
Absolute Summability ◽  
Fourier Integrals

We obtain the conditions for function that generates functional method and for the multiplier $\mu(y)$ that are sufficient for absolute summability of$$\int\limits_0^{\infty} \mu (y) B(y, t) dy$$where $\int\limits_0^{\infty} B(y, t) dy$ is the Fourier integral of a function $f(t) \in L_{(-\infty, \infty)}$.

scholarly journals Summation of trigonometric Fourier integrals by method of G.F. Voronoi

2021 ◽  
pp. 50
Author(s):  
L.G. Bojtsun
Keyword(s):  
Sufficient Conditions ◽  
Fourier Integral ◽  
Functional Method ◽  
Fourier Integrals

In this paper we establish sufficient conditions of summability, by functional method of G.F. Voronoi, of Fourier integral of a function $f(t) \in L_{(-\infty, \infty)}$.

scholarly journals Absolute summation of Fourier integrals with multiplier by G.F. Voronoi method

2021 ◽  
Vol 16 ◽  
pp. 35
Author(s):  
L.G. Bojtsun ◽  
S.V. Kocherga
Keyword(s):  
Sufficient Conditions ◽  
Fourier Integral ◽  
Functional Method ◽  
Summation Method ◽  
Voronoi Method ◽  
Fourier Integrals

We provide the theorem that is connected with functional method of G.F. Voronoi. We establish sufficient conditions for a function that generates the summation method of G.F. Voronoi, on function-multiplier, and on function $f(t)$, under which the Fourier integral of this function with multiplier is absolutely summable by the functional method of G.F. Voronoi.

On uniform asymptotic expansions of finite Laplace and Fourier integrals

1980 ◽  
Vol 85 (3-4) ◽  
pp. 299-305 ◽  
Author(s):  
Kusum Soni
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Fourier Integral ◽  
Uniform Asymptotic Expansion ◽  
Laplace Integrals ◽  
Uniform Asymptotic Expansions ◽  
Fourier Integrals

SynopsisA uniform asymptotic expansion of the Laplace integrals ℒ(f, s) with explicit remainder terms is given. This expansion is valid in the whole complex s−plane. In particular, for s = −ix, it provides the Fourier integral expansion.

A case of distinction between Fourier integrals and Fourier series

1927 ◽  
Vol 23 (7) ◽  
pp. 755-767
Author(s):  
Margaret Eleanor Grimshaw
Keyword(s):  
Fourier Series ◽  
Finite Type ◽  
Generating Function ◽  
Fourier Integral ◽  
Finite Range ◽  
Fourier Integrals

A Fourier integral is said to be of finite type if its generating function vanishes for all sufficiently large values of ¦x¦. Because the coefficient functions are defined by integrals over a finite range, the behaviour of such a Fourier integral usually resembles closely that of the corresponding series.

Strong Cesàro summability and statistical limit of fourier integrals

Analysis ◽  
2005 ◽  
Vol 25 (1) ◽  
Author(s):  
Ferenc Móricz
Keyword(s):  
Measurable Function ◽  
Integrable Function ◽  
Fourier Integral ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Statistical Limit ◽  
Locally Integrable Function ◽  
Fourier Integrals

AbstractIn our previous paper [2], we introduced the concept of statistical limit of a measurable function and that of strong Cesàro summability of a locally integrable function. As an application, we proved there that the Fourier integral of a function ƒ ∈ L(i) We prove that if ƒ ∈ L(ii) We complete and simplify the proof of [2, Statement (γ) of Theorem 3], which says that if ƒ ∈ L

l-1 summability of multiple Fourier integrals and positivity

1997 ◽  
Vol 122 (1) ◽  
pp. 149-172 ◽  
Author(s):  
HUBERT BERENS ◽  
YUAN XU
Keyword(s):  
Lower Bound ◽  
Fourier Integral ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Bochner’S Theorem ◽  
Bochner's Theorem ◽  
Sufficiency Condition ◽  
Central Result ◽  
Fourier Integrals

Let f∈L1(ℝd), and let fˆ be its Fourier integral. We study summability of the l-1 partial integral S(1)R, d(f; x)= ∫[mid ]v[mid ][les ]Reiv·xfˆ(v)dv, x∈ℝd; note that the integral ranges over the l1-ball in ℝd centred at the origin with radius R>0. As a central result we prove that for δ[ges ]2d−1 the l-1 Riesz (R, δ) means of the inverse Fourier integral are positive, the lower bound being best possible. Moreover, we will give an l-1 analogue of Schoenberg's modification of Bochner's theorem on positive definite functions on ℝd as well as an extention of Polya's sufficiency condition.

On the convergence of double Fourier integrals of functions of bounded variation on ℝ2

2016 ◽  
Vol 53 (3) ◽  
pp. 289-313
Author(s):  
Bhikha Lila Ghodadra ◽  
Vanda Fülöp
Keyword(s):  
Uniform Convergence ◽  
Bounded Variation ◽  
Fourier Integral ◽  
Functions Of Bounded Variation ◽  
Two Dimensional ◽  
Dirichlet Integrals ◽  
Fourier Integrals

We investigate the pointwise and uniform convergence of the symmetric rectangular partial (also called Dirichlet) integrals of the double Fourier integral of a function that is Lebesgue integrable and of bounded variation over ℝ2. Our theorem is a two-dimensional extension of a theorem of Móricz (see Theorem 3 in [10]) concerning the single Fourier integrals, which is more general than the two-dimensional extension given by Móricz himself (see Theorem 3 in [11]).

scholarly journals Absolute summability of conjugate Fourier integrals by Voronoi-Nerlund method

2021 ◽  
pp. 60
Author(s):  
N.I. Volkova ◽  
N.P. Ogol
Keyword(s):  
Absolute Summability ◽  
Fourier Integrals

We establish conditions of absolute summability of Fourier integrals and conjugate Fourier integrals by Voronoi-Nerlund method.

Fourier Integrals in Classical Analysis

1993 ◽  
Author(s):  
Christopher D. Sogge
Keyword(s):  
Classical Analysis ◽  
Fourier Integrals
Sign in / Sign up

Export Citation Format

Share Document