Interpolation by Harmonic Polynomials

Interpolation by Harmonic Polynomials PDF

Author: John Hamilton Curtiss

Publisher:

Published: 1961

Total Pages: 70

ISBN-13:

DOWNLOAD EBOOK →

Let Hn (u;z) denote the harmonic polynomial of degree at most n found by interpolation in 2n +1 points in a function u given on the boundary C of a region D of the complex z-plane. Explict formulas are derived for Hn in the case of interpolation on a circle and on an ellipse, and convergence is proved in these cases for arbitrary continuous boundary data. Various generalizations are indicated.

Interpolation with Polynomials to Boundary Values

Interpolation with Polynomials to Boundary Values PDF

Author: J. H. Curtiss

Publisher:

Published: 1968

Total Pages: 21

ISBN-13:

DOWNLOAD EBOOK →

The report reviews work that appear in the following papers: Transfinite diameter and harmonic polynomial interpolation; Faber polynomials and the Faber series; Complex Lagrange interpolation on a Jordan curve with cusps; Divergence of interpolation polynomials in the complex domain; Existence of Liouville numbers.

Polynomials and Harmonic Functions on Finite Fields

Polynomials and Harmonic Functions on Finite Fields PDF

Author:

Publisher:

Published: 2018

Total Pages: 0

ISBN-13:

DOWNLOAD EBOOK →

"The possibility of extending the generalized form of the Lagrange Interpolation Formula to function on finite fields is investigated. Following the proof in the classical we develop an interpolation formula for finite field polynomials using a "derivative" which is defined on these polynomials." -- Abstract.

Complex Analysis and Dynamical Systems III

Complex Analysis and Dynamical Systems III PDF

Author: Mark Lʹvovich Agranovskiĭ

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 482

ISBN-13: 0821841505

DOWNLOAD EBOOK →

The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Interpolation of Functions

Interpolation of Functions PDF

Author: J. Szabados

Publisher: World Scientific

Published: 1990

Total Pages: 328

ISBN-13: 9789971509156

DOWNLOAD EBOOK →

This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics.

Lectures on Complex Approximation

Lectures on Complex Approximation PDF

Author: GAIER

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 207

ISBN-13: 1461248140

DOWNLOAD EBOOK →

The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications. In the last ten or fifteen years, however, the situation has changed radically. First, a great deal of significant exper~en tal data became available. Then important contributions were made to the incorporation of general relativity into the framework of quantum theory. Finally, in the last three years, exciting devel opments took place which have placed general relativity, and all the concepts behind it, at the center of our understanding of par ticle physics and quantum field theory. Firstly, this is due to the fact that general relativity is really the "original non-abe lian gauge theory," and that our description of quantum field in teractions makes extensive use of the concept of gauge invariance. Secondly, the ideas of supersymmetry have enabled theoreticians to combine gravity with other elementary particle interactions, and to construct what is perhaps the first approach to a more finite quantum theory of gravitation, which is known as super gravity.

Selected Papers

Selected Papers PDF

Author: Joseph L. Walsh

Publisher: Springer Science & Business Media

Published: 2000-02-11

Total Pages: 734

ISBN-13: 9780387987828

DOWNLOAD EBOOK →

This volume is a selection from the 281 published papers of Joseph Leonard Walsh, former US Naval Officer and professor at University of Maryland and Harvard University. The nine broad sections are ordered following the evolution of his work. Commentaries and discussions of subsequent development are appended to most of the sections. Also included is one of Walsh's most influential works, "A closed set of normal orthogonal function," which introduced what is now known as "Walsh Functions".