The Integral Transformations

2000 ◽  
pp. 321-336
Author(s):  
Qi-keng Lu
Keyword(s):  
Integral Transformations

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Integral transforms for logharmonic mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hugo Arbeláez ◽  
Víctor Bravo ◽  
Rodrigo Hernández ◽  
Willy Sierra ◽  
Osvaldo Venegas
Keyword(s):  
Function Theory ◽  
Classical Problem ◽  
Integral Transforms ◽  
Geometric Function Theory ◽  
Integral Transformations ◽  
Geometric Function

AbstractBieberbach’s conjecture was very important in the development of geometric function theory, not only because of the result itself, but also due to the large amount of methods that have been developed in search of its proof. It is in this context that the integral transformations of the type $f_{\alpha }(z)=\int _{0}^{z}(f(\zeta )/\zeta )^{\alpha }\,d\zeta $ f α ( z ) = ∫ 0 z ( f ( ζ ) / ζ ) α d ζ or $F_{\alpha }(z)=\int _{0}^{z}(f'(\zeta ))^{\alpha }\,d\zeta $ F α ( z ) = ∫ 0 z ( f ′ ( ζ ) ) α d ζ appear. In this note we extend the classical problem of finding the values of $\alpha \in \mathbb{C}$ α ∈ C for which either $f_{\alpha }$ f α or $F_{\alpha }$ F α are univalent, whenever f belongs to some subclasses of univalent mappings in $\mathbb{D}$ D , to the case of logharmonic mappings by considering the extension of the shear construction introduced by Clunie and Sheil-Small in (Clunie and Sheil-Small in Ann. Acad. Sci. Fenn., Ser. A I 9:3–25, 1984) to this new scenario.

scholarly journals Special Issue of Symmetry: “Integral Transformations, Operational Calculus and Their Applications”

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1169
Author(s):  
Hari Mohan Srivastava
Keyword(s):  
Operational Calculus ◽  
Subject Area ◽  
Special Issue ◽  
Integral Transformations ◽  
The World ◽  
Different Parts

This Special Issue consists of a total of 14 accepted submissions (including several invited feature articles) to the Special Issue of the MDPI’s journal, Symmetry on the general subject-area of “Integral Transformations, Operational Calculus and Their Applications” from different parts of the world [...]

Diffraction of impulsive elastic waves by a fluid cylinder

1974 ◽  
Vol 75 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Ramanand Jha
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Line Source ◽  
Inviscid Fluid ◽  
Geometrical Theory ◽  
Shadow Zone ◽  
Integral Transformations ◽  
Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

Die Verwendung von Integraltransformationen in der Quantenchemie / The Application of Integral Transformations in Quantum Chemistry

1972 ◽  
Vol 27 (10) ◽  
pp. 1473-1478
Keyword(s):  
Quantum Chemistry ◽  
Integral Transformations ◽  
Gauss Transformation

Abstract Two possible cases of the introduction of a Gauss transformation are discussed. The FSGO method is able to be generalized by means of integral transformations. The application of these methods to the systems H, He and LiH has shown that the results are near the HF-limit, without having difficulties with SCF-iterations.

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