A quadratic‐phase integral operator for sets of generalized integrable functions

2020 ◽  
Author(s):  
Shrideh K. Q. Al‐Omari ◽  
Dumitru Baleanu
Keyword(s):  
Integral Operator ◽  
Quadratic Phase ◽  
Integrable Functions ◽  
Phase Integral

VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM

2006 ◽  
Vol 04 (04) ◽  
pp. 377-408 ◽  
Author(s):  
CLAUDIO CARMELI ◽  
ERNESTO DE VITO ◽  
ALESSANDRO TOIGO
Keyword(s):  
Integral Operator ◽  
Hilbert Spaces ◽  
Spectral Decomposition ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Integrable Functions ◽  
Kernel Hilbert Spaces ◽  
Vector Valued

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.

scholarly journals Certain Inequalities Involving Generalized Erdélyi-Kober Fractionalq-Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Praveen Agarwal ◽  
Soheil Salahshour ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Integrable Functions ◽  
Special Cases

In recent years, a remarkably large number of inequalities involving the fractionalq-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractionalq-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kober type fractionalq-integral operators. The cases of synchronous functions as well as of functions bounded by integrable functions are considered.

scholarly journals Riemann–Liouville Operator in Weighted Lp Spaces via the Jacobi Series Expansion

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 75 ◽  
Author(s):  
Maksim V. Kukushkin
Keyword(s):  
Integral Operator ◽  
Liouville Operator ◽  
Fractional Integral ◽  
Jacobi Polynomials ◽  
Fractional Integral Operator ◽  
Proved Theorem ◽  
Jacobi Series ◽  
Integrable Functions ◽  
Operator Action ◽  
Square Integrable Functions

In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann–Liouville fractional integral and derivative operators on a compact of the real axis. This approach has some advantages and allows us to complete the previously known results of the fractional calculus theory by means of reformulating them in a new quality. The proved theorem on the fractional integral operator action is formulated in terms of the Jacobi series coefficients and is of particular interest. We obtain a sufficient condition for a representation of a function by the fractional integral in terms of the Jacobi series coefficients. We consider several modifications of the Jacobi polynomials, which gives us the opportunity to study the invariant property of the Riemann–Liouville operator. In this direction, we have shown that the fractional integral operator acting in the weighted spaces of Lebesgue square integrable functions has a sequence of the included invariant subspaces.

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

Univalence criteria for a general integral operator

Filomat ◽  
2014 ◽  
Vol 28 (1) ◽  
pp. 11-19 ◽  
Author(s):  
Erhan Deniz
Keyword(s):  
Integral Operator ◽  
General Integral ◽  
Significant Relationships ◽  
General Integral Operator ◽  
Univalence Criteria

In this paper the author introduces a general integral operator and determines conditions for the univalence of this integral operator. Also, the significant relationships and relevance with other results are also given.

ON ABSOLUTELY HENSTOCK INTEGRABLE FUNCTIONS

1986 ◽  
Vol 12 (2) ◽  
pp. 524
Author(s):  
Chuan-Song ◽  
Peng-Yee
Keyword(s):  
Integrable Functions
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