On the theorem of Walsh-Runge

On the theorem of Walsh-Runge

A version of the classical holomorphic and meromorphic approximation therems by Behnke-Stein and Walsh is proved in the case of a general, not necessarily smooth, one-dimensional complex space. It contains all the known results, which are briefly reviewed.

Bibliographic Details
Main Author:	Alessandro Silva
Format:	Article
Language:	English
Published:	Sapienza Università Editrice 2014-01-01
Series:	Rendiconti di Matematica e delle Sue Applicazioni
Subjects:	holomorphic approximation meromorphic approximation
Online Access:	https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2014(3-4)/207-214.pdf

Similar Items

Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property
by: Manjul Gupta, et al.
Published: (2016-12-01)

Functional analysis, holomorphy and approximation theory II /
by: Zapata, Guido I.
Published: (1984)

Normal forms for singularities of one dimensional holomorphic vector fields
by: Antonio Garijo, et al.
Published: (2004-10-01)

ON CAUCHY PROBLEM SOLUTION FOR A HARMONIC FUNCTION IN A SIMPLY CONNECTED DOMAIN
by: E. A. Shirokova, et al.
Published: (2023-03-01)

An approximation theorem for rearrangements /
by: 295797 Chong, Kong-Ming, et al.
Published: (1978)

NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION
by: GHAZI ABDULLAH Madlol
Published: (2017-12-01)

STATCOM Model Using Holomorphic Embedding
by: Pradeep Singh, et al.
Published: (2019-01-01)

Representation of Some Ratios of Horn’s Hypergeometric Functions H<sub>7</sub> by Continued Fractions
by: Tamara Antonova, et al.
Published: (2023-07-01)

Some remarks on a theorem of Green
by: Abdessami ben Hmida Jalled, et al.
Published: (2022-12-01)

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function <i>H</i><sub>4</sub>(<i>a</i>,<i>b</i>;<i>c</i>,<i>d</i>;<i>z</i><sub>1</sub>,<i>z</i><sub>2</sub>) Ratios
by: Tamara Antonova, et al.
Published: (2023-03-01)

Nevanlinna’s Five Values Theorem on Annuli
by: Hong-Yan Xu, et al.
Published: (2016-02-01)

Uniqueness theorem on meromorphic functions and their difference operators
by: Dan Liu, et al.
Published: (2018-11-01)

Functional and Operatorial Equations Defined Implicitly and Moment Problems
by: Octav Olteanu
Published: (2024-01-01)

Symmetry and Asymmetry in Moment, Functional Equations, and Optimization Problems
by: Octav Olteanu
Published: (2023-07-01)

Sharp Real-Part Theorems [electronic book]: A Unified Approach/
by: 357224 Kresin, Gershon, et al.
Published: (2007)

Cauchy type generalizations of holomorphic mean value theorems
by: Anugraha Nidhi Mohapatra
Published: (2012-10-01)

POINTS OF RETRACTION INTO CONE AND VORONOVSKAYA TYPE THEOREMS
by: Yury Abakumov, et al.
Published: (2015-10-01)

Design of Multi-Dimensional Recursive Systems through Pad'e Type Rational Approximation
by: Valeri V. Vavilov, et al.
Published: (2002-06-01)

Solving system of Euler's equations using Runge –Kutta methods
by: Aseel Al_Ameely, et al.
Published: (2023-12-01)

A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions
by: Le Phuong Quan
Published: (2018-10-01)

Pade and rational approximation : theory and applications/
by: Conference on Rational Approximation with Emphasis on Applications of Pade Approximants, (1976 : Tampa, Fla.), et al.
Published: (1977)

On the solution of some minimax problems /
by: 196299 Bertsekas, Dimitri P.

Pade approximation and its applications Bad Honnef 1983 /
by: Werner, H.
Published: (1984)

On Montessus de Ballore’s theorem for simultaneous Padé-Faber approximants
by: Bosuwan Nattapong
Published: (2018-04-01)

On Estimation of the Remainder Term in New Asymptotic Expansions in the Central Limit Theorem
by: Vitaly Sobolev, et al.
Published: (2023-04-01)

Various-Order Low-Pass Filter with the Electronic Change of Its Approximation
by: Lukas Langhammer, et al.
Published: (2023-09-01)

Rational Approximations of Arbitrary Order: A Survey
by: José Daniel Colín-Cervantes, et al.
Published: (2021-12-01)

Approximate Regular Modules
by: Baghdad Science Journal
Published: (2011-12-01)

Direct and inverse theorems for Bernstein polynomials with inner singularities
by: Wen-ming Lu, et al.
Published: (2012-10-01)

The equidistribution theory of holomorphic curves /
by: 309957 Wu, Hung-Hsi
Published: (1970)

Holomorphic functions of the variable /
by: 236767 Colombo, Serge
Published: (1983)

On the extension of (LH)p - functions in polydics /
by: 306051 Chee, P. S.
Published: (1985)

Advances in holomorphy/
by: Seminario de Holomorfia, Universidade Federal do Rio de Janeiro, September 26-28, 1977, et al.
Published: (1979)

Approximation of Functions in Lp, Î± (I) (0 < p < 1)
by: Saheb K. Jassim, et al.
Published: (2017-04-01)

Fatou type theorems : maximal functions and approach regions /
by: Di Biase, Faust 1962-
Published: (1998)

Approximation theorems for the Gauss-Weierstrass singular integral
by: B. FIRLEJ, et al.
Published: (1995-05-01)

Mean value theorem for holomorphic functions
by: Devrim Cakmak, et al.
Published: (2012-02-01)

Approximation-Aware Design of an Image-Based Control System
by: Sayandip De, et al.
Published: (2020-01-01)

Notes on Approximately Pure Submodules
by: Baghdad Science Journal
Published: (2013-12-01)

Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces
by: A.S. Serdyuk, et al.
Published: (2021-12-01)