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

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.

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Integration of polar-analytic functions and applications to Boas’ differentiation formula and Bernstein’s inequality in Mellin setting

Bollettino dell Unione Matematica Italiana ◽

10.1007/s40574-020-00226-9 ◽

2020 ◽

Vol 13 (4) ◽

pp. 503-514 ◽

Cited By ~ 1

Author(s):

Carlo Bardaro ◽

Paul L. Butzer ◽

Ilaria Mantellini ◽

Gerhard Schmeisser

Keyword(s):

Analytic Functions ◽

Integral Formula ◽

Type Inequality ◽

General Version ◽

Residue Theorem ◽

Bernstein Type ◽

Bernstein’S Inequality ◽

Differentiation Formula ◽

Bernstein Type Inequality ◽

Cauchy’S Integral Formula

Abstract We establish a general version of Cauchy’s integral formula and a residue theorem for polar-analytic functions, employing the new notion of logarithmic poles. As an application, a Boas-type differentiation formula in Mellin setting and a Bernstein-type inequality for polar Mellin derivatives are deduced.

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

Numerical Algorithms ◽

10.1007/s11075-018-0548-5 ◽

2018 ◽

Vol 81 (1) ◽

pp. 293-312 ◽

Cited By ~ 1

Author(s):

Rashad M. Asharabi

Keyword(s):

Analytic Functions ◽

Sampling Formula ◽

Derivatives Of ◽

Gaussian Sampling

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Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions

Numerical Algorithms ◽

10.1007/s11075-020-00939-0 ◽

2020 ◽

Author(s):

R. M. Asharabi ◽

J. Prestin

Keyword(s):

Analytic Functions ◽

Partial Derivatives ◽

Sampling Formula ◽

Derivatives Of

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The identity theorem for analytic functions

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(74)90059-6 ◽

1974 ◽

Vol 45 (3) ◽

pp. 682-683 ◽

Cited By ~ 1

Author(s):

Alexander Abian

Keyword(s):

Analytic Functions ◽

Identity Theorem

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A NOTE ON INTERPOLATION OF PERMUTATIONS OF A SUBSET OF A FINITE FIELD

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972714000173 ◽

2014 ◽

Vol 90 (2) ◽

pp. 213-219 ◽

Cited By ~ 1

Author(s):

CHRIS CASTILLO ◽

ROBERT S. COULTER ◽

STEPHEN SMITH

Keyword(s):

Finite Field ◽

Finite Fields ◽

Interpolation Formula ◽

Permutation Polynomials ◽

Classical Interpolation ◽

Compositional Inverse

AbstractWe determine several variants of the classical interpolation formula for finite fields which produce polynomials that induce a desirable mapping on the nonspecified elements, and without increasing the number of terms in the formula. As a corollary, we classify those permutation polynomials over a finite field which are their own compositional inverse, extending work of C. Wells.

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Sequences and Series of Analytic Functions, the Residue Theorem

Universitext - Complex Analysis ◽

10.1007/3-540-30823-7_4 ◽

2006 ◽

pp. 105-194

Keyword(s):

Analytic Functions ◽

Residue Theorem

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Optimization of Interpolation Algorithm in Survey Calculation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.831.450 ◽

2013 ◽

Vol 831 ◽

pp. 450-454

Author(s):

Tie Yan ◽

Ji Jun Li ◽

Xing Bao Gao ◽

Xiao Feng Sun ◽

Shuai Shao

Keyword(s):

Interpolation Method ◽

Interpolation Formula ◽

Field Work ◽

Petroleum Engineering ◽

Radius Of Curvature ◽

Curvature Radius ◽

Interpolation Algorithm ◽

Theory Analysis ◽

Oil Exploitation ◽

Classical Interpolation

The interpolation algorithm in survey calculation is widely used in petroleum engineering, and it is different from the general mathematical interpolation. Along with the development of oil exploitation, various special type of well begin to appear, but the original interpolation method can not meet the needs of the field work. So the paper according to classical interpolation model of the interpolation algorithm, the three optimization intercalation models the curvature radius of curvature, minimum curvature, and natural curve were figured out. Theory analysis and results show that optimized interpolation formula the paper established can meet all kinds of optimization calculation of the inclined interpolation needs.

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FUNCTIONS WITH SPLINE SPECTRA AND THEIR APPLICATIONS

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691310003432 ◽

2010 ◽

Vol 08 (02) ◽

pp. 197-223 ◽

Cited By ~ 8

Author(s):

QIUHUI CHEN ◽

CHARLES A. MICCHELLI ◽

YI WANG

Keyword(s):

Real Axis ◽

Real Line ◽

Analytic Functions ◽

Signal Analysis ◽

Sinc Function ◽

The Real ◽

Sampling Formula

In this paper, we introduce a family of real-valued functions which have spline spectra. They extend the well-known Sinc function and generally are the restrictions to the real line of analytic functions in a strip containing the real axis. We investigate various properties of these functions including those related to interpolation, orthogonality, and stability. Moreover, a sampling formula is provided for their construction and some applications for signal analysis are given.

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