Asymptotic behaviour of the H-transform in the complex domain

1987 ◽  
Vol 102 (3) ◽  
pp. 533-552 ◽  
Author(s):  
Richard D. Carmichael ◽  
Ram S. Pathak
Keyword(s):  
Asymptotic Behaviour ◽  
Half Plane ◽  
Complex Variable ◽  
Structure Theorem ◽  
Generalized Functions ◽  
Complex Domain ◽  
The Right ◽  
Abelian Theorems

AbstractAbelian theorems for the H-transform of functions and generalized functions are obtained as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Quasi-asymptotic behaviour (q.a.b.) of the H-transformable generalized functions is defined. A structure theorem for generalized functions possessing q.a.b. is proved and is applied to obtain the asymptotic behaviour of the H-transform of generalized functions having q.a.b. The theorems are illustrated by examples.

scholarly journals Final Value Abelian Theorems for the Stieltjes Transform of Generalized Functions

2011 ◽  
Vol 127 (2) ◽  
pp. 179-183
Author(s):  
RICHARD D. CARMICHAEL
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Equivalent Form ◽  
Generalized Functions ◽  
Stieltjes Transform ◽  
Initial Value ◽  
Final Value ◽  
The Right ◽  
Abelian Theorems

Abstract Limit results are obtained for the Stieltjes transform of generalized functions as the domain complex variable s approaches ∞ (final value results) in the right half plane. These results are of equivalent form as results for the transform as s approaches 0 (initial value results) in the right half plane.

scholarly journals Abelian theorems for Whittaker transforms

1987 ◽  
Vol 10 (3) ◽  
pp. 417-431 ◽  
Author(s):  
Richard D. Carmichael ◽  
R. S. Pathak
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Absolute Value ◽  
Final Value ◽  
The Right ◽  
Abelian Theorems

Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches0or∞in absolute value inside a wedge region in the right half plane.

scholarly journals S-plane analysis for the fundamental problems of a stretched infinite plate weakened by curvilinear holes

2004 ◽  
Vol 2004 (24) ◽  
pp. 1255-1265
Author(s):  
I. S. Ismail
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Infinite Plate ◽  
Complex Variable Methods ◽  
Plane Analysis ◽  
Special Cases ◽  
Different Shapes ◽  
The Right ◽  
Curvilinear Holes

Complex variable methods are used to obtain exact and closed expressions for Goursat's functions for the stretched infinite plate weakened by two inner holes which are free from stresses. The plate considered is conformally mapped on the area of the right half-plane. Previous work is considered as special cases of this work. Cases of different shapes of holes are included. Also, many new cases are discussed using this mapping.

scholarly journals Abelian theorems for the stieltjes transform of functions, II

1981 ◽  
Vol 4 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Richard D. Carmichael ◽  
Elmer K. Hayashi
Keyword(s):  
Half Plane ◽  
Stieltjes Transform ◽  
Final Value ◽  
Abelian Theorem ◽  
The Right ◽  
Abelian Theorems

An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches∞) is used to infer the behavior of the transform as its domain variable approaches zero (approaches∞). We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variablesof the transform is complex in the right half plane; and the initial (final) value Abelian theorems are obtained as|s|→0(|s|→∞)within an arbitrary wedge in the right half plane.

scholarly journals Recent developments on the Stieltjes transform of generalized functions

1987 ◽  
Vol 10 (4) ◽  
pp. 641-670 ◽  
Author(s):  
Ram Sankar Pathak ◽  
Lokenath Debnath
Keyword(s):  
Final Section ◽  
Generalized Functions ◽  
Stieltjes Transform ◽  
Poisson Transform ◽  
Open Questions ◽  
The Laplace Transform ◽  
Recent Developments ◽  
The Subject ◽  
Abelian Theorems ◽  
Stieltjes Transforms

This paper is concerned with recent developments on the Stieltjes transform of generalized functions. Sections 1 and 2 give a very brief introduction to the subject and the Stieltjes transform of ordinary functions with an emphasis to the inversion theorems. The Stieltjes transform of generalized functions is described in section 3 with a special attention to the inversion theorems of this transform. Sections 4 and 5 deal with the adjoint and kernel methods used for the development of the Stieltjes transform of generalized functions. The real and complex inversion theorems are discussed in sections 6 and 7. The Poisson transform of generalized functions, the iteration of the Laplace transform and the iterated Stieltjes transfrom are included in sections 8, 9 and 10. The Stieltjes transforms of different orders and the fractional order integration and further generalizations of the Stieltjes transform are discussed in sections 11 and 12. Sections 13, 14 and 15 are devoted to Abelian theorems, initial-value and final-value results. Some applications of the Stieltjes transforms are discussed in section 16. The final section deals with some open questions and unsolved problems. Many important and recent references are listed at the end.

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

scholarly journals Analyticity of semigroups on the right half-plane

2017 ◽  
Vol 448 (2) ◽  
pp. 750-766 ◽  
Author(s):  
Mark Elin ◽  
Fiana Jacobzon
Keyword(s):  
Half Plane ◽  
The Right
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