scholarly journals Pseudo-differential equations connected with p-adic forms and local zeta functions

2004 ◽  
Vol 70 (1) ◽  
pp. 73-86 ◽  
Author(s):  
W. A. Zuniga-Galindo
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Zeta Functions ◽  
Fundamental Solutions ◽  
Pseudo Differential Operator ◽  
Arbitrary Degree ◽  
Local Zeta Functions

We study the asymptotics of fundamental solutions of p-adic pseudo-differential equations of type where f(∂,β) is a pseudo-differential operator with symbol , f is a form of arbitrary degree with coefficients in a p-adic field, λ ≥ 0, and g is a Schwartz-Bruhat function.

scholarly journals On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations

2015 ◽  
Vol 7 (1) ◽  
pp. 101-107 ◽  
Author(s):  
M.M. Osypchuk
Keyword(s):  
Cauchy Problem ◽  
Differential Operator ◽  
Euclidean Space ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Stable Process ◽  
Pseudo Differential Operator ◽  
The Cauchy Problem ◽  
Vector Valued Function ◽  
Vector Valued

A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a pseudo-differential operator whose symbol is given by $-c|\lambda|^\alpha$, were the constants $\alpha\in(1,2)$ and $c>0$ are fixed. The vector-valued operator $\mathbf{B}$ has the symbol $2ic|\lambda|^{\alpha-2}\lambda$. We construct a fundamental solution of the equation $u_t=(\mathbf{A}+(a(\cdot),\mathbf{B}))u$ with a continuous bounded vector-valued function $a$.

scholarly journals PSEUDO-DIFFERENTIAL OPERATORS AND EQUATIONS IN A DISCRETE HALF-SPACE

2018 ◽  
Vol 23 (3) ◽  
pp. 492-506 ◽  
Author(s):  
Vladimir B. Vasilyev ◽  
Alexander V. Vasilyev
Keyword(s):  
Differential Operator ◽  
General Solution ◽  
Differential Equations ◽  
Half Space ◽  
Differential Operators ◽  
Pseudo Differential Operator ◽  
Pseudo Differential Operators ◽  
Special Case

We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space. The theorem on a general solution of such equations is proved for a special case.

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

A nonlocal problem for a differential operator of even order with involution

2020 ◽  
Vol 26 (2) ◽  
pp. 297-307
Author(s):  
Petro I. Kalenyuk ◽  
Yaroslav O. Baranetskij ◽  
Lubov I. Kolyasa
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riesz Basis ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Nonlocal Problem ◽  
Even Order

AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

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