<abstract xmlns="http://www.w3.org/1999/xhtml"> J. Korous reached an important result for general orthogonal polynomials in one variable. He dealt with the boundedness and uniform boundedness of polynomials { Pn(x)}∞n=0 orthonormal with the weight function h(x) = δ(x) ̃h(x), where ̃h(x) is the weight function of another system of polynomials { ̃Pn(x) }∞n=0 orthonormal in the same interval andδ(x) ≥ δ0 > 0 is a certain function. We generalize this result for orthogonal polynomials in two variables multiplying their weight function h(x, y) by a polynomial, dividing h(x, y) by a polynomial, and multiplying h(x, y) with separated variables by a certain function δ(x, y). </abstract>

J. Korous reached an important result for general orthogonal polynomials in one variable. He dealt with the boundedness and uniform boundedness of polynomials { Pn(x)}∞n=0 orthonormal with the weight function h(x) = δ(x) ̃h(x), where ̃h(x) is the weight function of another system of polynomials { ̃Pn(x) }∞n=0 orthonormal in the same interval andδ(x) ≥ δ0 > 0 is a certain function. We generalize this result for orthogonal polynomials in two variables multiplying their weight function h(x, y) by a polynomial, dividing h(x, y) by a polynomial, and multiplying h(x, y) with separated variables by a certain function δ(x, y).

Korous Type Inequalities for Orthogonal Polynomials in two Variables

Department of Applied MathematicsFaculty of Mechanical Engineering University of Zilina Univerzitna 8215/1SK–010-26 Zilina SLOVAKIA

Department of Applied MathematicsFaculty of Mechanical Engineering University of Zilina Univerzitna 8215/1SK-010-26 Zilina SLOVAKIA

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Korous Type Inequalities for Orthogonal Polynomials in two Variables"}

J. Korous reached an important result for general orthogonal polynomials in one variable. He dealt with the boundedness and uniform boundedness of polynomials...

Korous Type Inequalities for Orthogonal Polynomials in two Variables

Published Online: Aug 15, 2014

Page range: 1 - 12

Received: Jan 10, 2012

DOI: https://doi.org/10.2478/tmmp-2014-0001

Keywords
Korous theorem, orthogonal polynomials in two variables, weight function, boundedness

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Korous Type Inequalities for Orthogonal Polynomials in two Variables

Published Online: Aug 15, 2014

Page range: 1 - 12

Received: Jan 10, 2012

DOI: https://doi.org/10.2478/tmmp-2014-0001

KeywordsKorous theorem, orthogonal polynomials in two variables, weight function, boundedness

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Korous theorem, orthogonal polynomials in two variables, weight function, boundedness