The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions

2018 ◽  
Vol 81 (1) ◽  
pp. 293-312 ◽  
Author(s):  
Rashad M. Asharabi
Keyword(s):  
Analytic Functions ◽  
Sampling Formula ◽  
Derivatives Of ◽  
Gaussian Sampling

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

On Hadamard compositions of Gelfond-Leont'ev derivatives of analytic functions

2021 ◽  
pp. 67-80
Author(s):  
Myroslav Mykolayovych Sheremeta ◽  
◽  
Oksana Myroslavivna Mulyava ◽  
Keyword(s):  
Analytic Functions ◽  
Derivatives Of

Hadamard compositions of Gelfond–Leont’ev derivatives of analytic functions

2020 ◽  
Vol 249 (5) ◽  
pp. 769-785
Author(s):  
Myroslav M. Sheremeta ◽  
Oksana M. Mulyava
Keyword(s):  
Analytic Functions ◽  
Derivatives Of

scholarly journals Valiron’s Interpolation Formula and a Derivative Sampling Formula in the Mellin Setting Acquired via Polar-Analytic Functions

2020 ◽  
Vol 20 (3-4) ◽  
pp. 629-652
Author(s):  
Carlo Bardaro ◽  
Paul L. Butzer ◽  
Ilaria Mantellini ◽  
Gerhard Schmeisser
Keyword(s):  
Analytic Functions ◽  
Main Tool ◽  
Interpolation Formula ◽  
Residue Theorem ◽  
Differentiation Formula ◽  
Sampling Formula ◽  
Bernstein Spaces ◽  
Derivative Sampling ◽  
Classical Interpolation ◽  
Identity Theorem

AbstractIn this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity theorem in Mellin–Bernstein spaces are obtained. The main tool in the proofs is a residue theorem for polar-analytic functions.

Some inequalities satisfied by the integrals or derivatives of real or analytic functions

1935 ◽  
Vol 39 (1) ◽  
pp. 677-695 ◽  
Author(s):  
G. H. Hardy ◽  
E. Landau ◽  
J. E. Littlewood
Keyword(s):  
Analytic Functions ◽  
Derivatives Of

scholarly journals EXTREME POINTS OF INTEGRAL FAMILIES OF ANALYTIC FUNCTIONS

2013 ◽  
Vol 94 (2) ◽  
pp. 202-221
Author(s):  
KEIKO DOW ◽  
D. R. WILKEN
Keyword(s):  
Analytic Functions ◽  
Compact Convex ◽  
Extreme Points ◽  
Starlike Functions ◽  
Extremal Problems ◽  
Kernel Functions ◽  
Closed Convex Hull ◽  
New Class ◽  
Geometric Function ◽  
Derivatives Of

AbstractExtreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a two-parameter collection of kernel functions integrated against measures on the torus. For specific choices of the parameters many families from classical geometric function theory are included. These families include the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others. The main result introduces a surprising new class of extreme points.

scholarly journals Boundary behavior of derivatives of analytic functions.

1992 ◽  
Vol 39 (1) ◽  
pp. 129-143 ◽  
Author(s):  
Sheldon Axler ◽  
Ke He Zhu
Keyword(s):  
Analytic Functions ◽  
Boundary Behavior ◽  
Derivatives Of
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