Causal propagator as boundary value of the analytic function in coordinate space

1969 ◽  
Vol 11 (1) ◽  
pp. 139-151
Author(s):  
Jerzy Lukierski
Keyword(s):  
Analytic Function ◽  
Boundary Value ◽  
Coordinate Space

scholarly journals Giải bài toán Carleman suy rộng trên trục thực bằng phương pháp chiếu lặp trên cơ sở phép chiếu bình phương tối thiểu

2018 ◽  
Vol 6 (1) ◽  
pp. 4-11
Author(s):  
Le Xuan Quang
Keyword(s):  
Analytic Function ◽  
Iterative Method ◽  
Real Axis ◽  
Half Plane ◽  
Boundary Value ◽  
Continuous Functions ◽  
Lower Half Plane ◽  
Hölder Continuous ◽  
Carleman Problem ◽  
Hölder Continuous Functions

 In this paper the projection iterative method is used for solving the generalized Carleman problem A(t) F+(t) + B(t) F+(-t) + C(t) F-(t) = h(t), tÎR Where R is the real axis; A(t), B(t), C(t) are Holder continuous functions;  h(t)ÎL2, and  F+(t), F-(t) is a boundary value of analytic function upper (lower) half-plane.

Piecewise continuous solutions of pseudoparabolic equations in two space dimensions

1978 ◽  
Vol 81 (1-2) ◽  
pp. 153-173 ◽  
Author(s):  
Heinrich Begehr ◽  
Robert P. Gilbert
Keyword(s):  
Analytic Function ◽  
Boundary Value Problem ◽  
Analytic Functions ◽  
Function Theory ◽  
Boundary Value ◽  
Cauchy Type ◽  
Bounded Solutions ◽  
Pseudoparabolic Equation ◽  
Cauchy Type Integral ◽  
Type Integral

SynopsisHere the Riemann boundary value problem-well known in analytic function theory as the problem to find entire analytic functions having a prescribed jump across a given contour-is solved for solutions of a pseudoparabolic equation which is derived from the complex differential equation of generalized analytic function theory. The general solution is given by use of the generating pair of the corresponding class of generalized analytic functions which gives rise to a representation for special bounded solutions of the pseudoparabolic equation. These solutions are obtained by linear integral equations one of which is given by a development of the generalized fundamental kernels of generalized analytic functions and which leads to a Cauchy-type integral representation. The bounded solutions are needed to transform the general boundary value problem (of non-negative index) with arbitrary initial data into a homogeneous problem which can easily be solved by the Cauchy-type integral (if the index is zero).

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