Generalized Derivatives of an Arbitrary Order and the Boundary Properties of Differentiated Poisson Integrals for the Half-Space

2000 ◽  
Vol 7 (2) ◽  
pp. 387-400
Author(s):  
S. Topuria
Keyword(s):  
Half Space ◽  
Arbitrary Order ◽  
Generalized Derivatives ◽  
Spherical Derivative ◽  
Poisson Integrals ◽  
Several Variables ◽  
Integral Density ◽  
Boundary Properties ◽  
Generalized Differential ◽  
Derivatives Of

Abstract The notions of a generalized differential and a generalized spherical derivative of an arbitrary order are introduced for a function of several variables and Fatou type theorems are proved on the boundary properties of partial derivatives of an arbitrary order of the Poisson integral for the half-space, when the integral density has a generalized differential or a generalized spherical derivative.

Boundary Properties of Second-Order Partial Derivatives of the Poisson Integral for a Half-Space

1998 ◽  
Vol 5 (4) ◽  
pp. 385-400
Author(s):  
S. Topuria
Keyword(s):  
Half Space ◽  
Second Order ◽  
Poisson Integral ◽  
Partial Derivatives ◽  
Boundary Properties ◽  
Derivatives Of

Abstract The boundary properties of second-order partial derivatives of the Poisson integral are studied for a half-space .

Boundary Properties of First-Order Partial Derivatives of the Poisson Integral for the Half-Space

1997 ◽  
Vol 4 (6) ◽  
pp. 585-600
Author(s):  
S. Topuria
Keyword(s):  
Half Space ◽  
Poisson Integral ◽  
Partial Derivatives ◽  
First Order ◽  
Boundary Properties ◽  
Derivatives Of

Abstract Boundary properties of first-order partial derivatives of the Poisson integral are studied in the half-space .

scholarly journals CONSTRAINT ALGEBRAS IN GAUGE-INVARIANT SYSTEMS

1995 ◽  
Vol 10 (28) ◽  
pp. 4087-4105 ◽  
Author(s):  
KH. S. NIROV
Keyword(s):  
Wide Class ◽  
Arbitrary Function ◽  
Arbitrary Order ◽  
Local Symmetry ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Constraint Algebra ◽  
Derivatives Of

A Hamiltonian description is constructed for a wide class of mechanical systems having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order. The Poisson brackets of the Hamiltonian and constraints with each other and with an arbitrary function are explicitly obtained. The constraint algebra is proved to be of the first class.

scholarly journals Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Jianfei Wang
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Arbitrary Order ◽  
Complex Banach Space ◽  
Holomorphic Mappings ◽  
Partial Derivatives ◽  
Carathéodory Metric ◽  
Homogeneous Ball ◽  
Derivatives Of

LetBXbe the unit ball in a complex Banach spaceX. AssumeBXis homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ballBntoBXassociated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.

An Analytical Solution of the Generalized Phase-Lagging Equation for Ultra-Fast Heat Transfer in One-Dimensional Semi-Infinite Domain

2012 ◽  
Author(s):  
Vladimir Kulish ◽  
Kirill V. Poletkin
Keyword(s):  
Analytical Solution ◽  
Domain Boundary ◽  
Integral Form ◽  
Solution Procedure ◽  
Generalized Derivatives ◽  
Infinite Domain ◽  
One Dimensional ◽  
Confluent Hypergeometric Functions ◽  
The Laplace Transform ◽  
Derivatives Of

The paper presents an integral solution of the generalized one-dimensional phase-lagging heat equation with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of non-integer orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the solution procedure, upon applying the Laplace transform to the original transport equation. The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the temperature and heat flux. The solution is valid everywhere within the domain, including the domain boundary.

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