scholarly journals Integral representations for Padé-type operators

2002 ◽  
Vol 2 (2) ◽  
pp. 51-69
Author(s):  
Nicholas J. Daras
Keyword(s):  
Fourier Series ◽  
Explicit Form ◽  
Harmonic Functions ◽  
Integral Operators ◽  
Integral Representations ◽  
Open Disk ◽  
Integral Formulas ◽  
Convergence Results ◽  
Do So

The main purpose of this paper is to consider an explicit form of the Padé-type operators. To do so, we consider the representation of Padé-type approximants to the Fourier series of the harmonic functions in the open disk and of theL p-functions on the circle by means of integral formulas, and, then we define the corresponding Padé-type operators. We are also oncerned with the properties of these integral operators and, in this connection, we prove some convergence results.

scholarly journals Integral representations of solutionsof Riquier for polyharmonic equations in n-dimensional ball

2017 ◽  
Vol 21 (6) ◽  
pp. 27-39
Author(s):  
E.V. Borodacheva ◽  
V.B. Sokolovskiy
Keyword(s):  
Harmonic Functions ◽  
Integral Operators ◽  
Integral Representations ◽  
The Third ◽  
Polyharmonic Equations ◽  
Dimensional Ball ◽  
Harmonic Equation

The solution of Riquier’s problem - the problem of finding in n-dimensional ball of solving k + 1 - harmonic equation for given values on the boundary of the desired solution u and powers of the Laplacian from one to k inclusive of this decision is obtained. The first part provides an exact statement of the problem, the main result (form of the solution of it), and the idea of this proof is stated. The second part introduces a family of some differential and integral operators in the space of harmonic functions in the ball used in the proof of the main result; some properties of these operators are set. The content of the third part is the proof of the main result. It is based on the properties of operators introduced in the second part.

A Maximum Principle for Dirichlet-Finite Harmonic Functions on Riemannian Spaces

1970 ◽  
Vol 22 (4) ◽  
pp. 855-862
Author(s):  
Y. K. Kwon ◽  
L. Sario
Keyword(s):  
Maximum Principle ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Decomposition Theorem ◽  
Higher Dimensions ◽  
Integral Representations ◽  
Classification Theory ◽  
Topological Properties ◽  
Harmonic Decomposition ◽  
Bounded Harmonic Functions

Representations of harmonic functions by means of integrals taken over the harmonic boundary ΔR of a Riemann surface R enable one to study the classification theory of Riemann surfaces in terms of topological properties of ΔR (cf. [6; 4; 1; 7]). In deducing such integral representations, essential use is made of the fact that the functions in question attain their maxima and minima on ΔR.The corresponding maximum principle in higher dimensions was discussed for bounded harmonic functions in [3]. In the present paper we consider Dirichlet-finite harmonic functions. We shall show that every such function on a subregion G of a Riemannian N-space R attains its maximum and minimum on the set , where ∂G is the relative boundary of G in R and the closures are taken in Royden's compactification R*. As an application we obtain the harmonic decomposition theorem relative to a compact subset K of R* with a smooth ∂(K ∩ R).

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

scholarly journals Pathway Fractional Integral Formulas Involving S-Function in the Kernel

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Hafte Amsalu ◽  
Biniyam Shimelis ◽  
D. L. Suthar
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Integral Formulas

In this paper, we present several composition formulae of pathway fractional integral operators connected with S-function. Here, we point out important links to known outcomes for some specific cases with our key results.

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