On the completeness of sine and cosine systems in the space of integrable functions

2018 ◽  
Author(s):  
Evgenii Ivanovich Moiseev ◽  
Denis Anatol'evich Gulyaev
Keyword(s):  
Integrable Functions ◽  
Space Of Integrable Functions

scholarly journals Certain fundamental properties of generalized natural transform in generalized spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shrideh Khalaf Al-Omari ◽  
Serkan Araci
Keyword(s):  
Inversion Formula ◽  
Acta Math ◽  
Generalized Functions ◽  
General Nature ◽  
Qualitative Behavior ◽  
Fundamental Properties ◽  
Integrable Functions ◽  
Extended Operator ◽  
Definition Of ◽  
Space Of Integrable Functions

AbstractThis paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

scholarly journals On linear singular functional-differential equations in one functional space

2004 ◽  
Vol 2004 (7) ◽  
pp. 567-575 ◽  
Author(s):  
Andrei Shindiapin
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Functional Space ◽  
Integrable Functions ◽  
The Cauchy Problem ◽  
Functional Differential ◽  
Space Of Integrable Functions ◽  
Special Space

We use a special space of integrable functions for studying the Cauchy problem for linear functional-differential equations with nonintegrable singularities. We use the ideas developed by Azbelev and his students (1995). We show that by choosing the functionψgenerating the space, one can guarantee resolubility and certain behavior of the solution near the point of singularity.

scholarly journals The conjugation operator onAq(G)

2003 ◽  
Vol 2003 (37) ◽  
pp. 2345-2347
Author(s):  
Sanjiv Kumar Gupta
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Compact Abelian Group ◽  
Bounded Operator ◽  
Conjugation Operator ◽  
Integrable Functions ◽  
The Fourier Transform ◽  
Space Of Integrable Functions

Letq>2. We prove that the conjugation operatorHdoes not extend to a bounded operator on the space of integrable functions defined on any compact abelian group with the Fourier transform inlq.

scholarly journals Multipliers on spaces of functions on compact groups with p-summable Fourier transforms

1993 ◽  
Vol 47 (3) ◽  
pp. 435-442 ◽  
Author(s):  
Sanjiv Kumar Gupta ◽  
Shobha Madan ◽  
U.B. Tewari
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Fourier Transforms ◽  
Dual Group ◽  
Compact Groups ◽  
Circle Group ◽  
Integrable Functions ◽  
Space Of Integrable Functions

Let G be a compact abelian group with dual group Γ. For 1 ≤ p < ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.

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