scholarly journals Second-order differential superordination for analytic functions in the upper half-plane

2017 ◽  
Vol 10 (10) ◽  
pp. 5271-5280 ◽  
Author(s):  
Huo Tang ◽  
H. M. Srivastava ◽  
Guan-Tie Deng ◽  
Shu-Hai Li
Keyword(s):  
Half Plane ◽  
Analytic Functions ◽  
Second Order ◽  
Differential Superordination ◽  
Upper Half Plane

scholarly journals Differential Subordination Results for Analytic Functions in the Upper Half-Plane

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huo Tang ◽  
M. K. Aouf ◽  
Guan-Tie Deng ◽  
Shu-Hai Li
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Upper Half Plane ◽  
Admissible Functions

There are many articles in the literature dealing with differential subordination problems for analytic functions in the unit disk, and only a few articles deal with the above problems in the upper half-plane. In this paper, we aim to derive several differential subordination results for analytic functions in the upper half-plane by investigating certain suitable classes of admissible functions. Some useful consequences of our main results are also pointed out.

scholarly journals A discrete analogue of the Paley-Wiener theorem for bounded analytic functions in a half plane

1977 ◽  
Vol 23 (3) ◽  
pp. 376-378
Author(s):  
Doron Zeilberger
Keyword(s):  
Analytic Function ◽  
Half Plane ◽  
Analytic Functions ◽  
Complex Analysis ◽  
Discrete Analogue ◽  
Bounded Analytic Functions ◽  
Bounded Analytic Function ◽  
Wiener Theorem ◽  
Upper Half Plane

In this note we prove a discrete analogue to the following Paley–Weiner theorem: Let f be the restriction to the line of a bounded analytic function in the upper half plane; then the spectrum of f is contained in ([0, ∈). The discrete analogue of complex analysis is the theory of discrete analytic functions invented by Lelong-Ferrand (1944) and developed by Duffin (1956) and others.

scholarly journals On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve

2014 ◽  
Vol 57 (2) ◽  
pp. 381-389
Author(s):  
Adrian Łydka
Keyword(s):  
Functional Equation ◽  
Meromorphic Function ◽  
Elliptic Curve ◽  
Explicit Formula ◽  
Half Plane ◽  
Complex Plane ◽  
Möbius Function ◽  
Mobius Function ◽  
Upper Half Plane ◽  
Explicit Formulae

AbstractWe study analytic properties function m(z, E), which is defined on the upper half-plane as an integral from the shifted L-function of an elliptic curve. We show that m(z, E) analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for m(z, E) in the strip |ℑz| < 2π.

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.

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