In: Tatra Mountains Mathematical Publications, vol. 58, no. 1
Branislav Ftorek - Pavol Oršanský
Detaily:
Rok, strany: 2014, 1 - 12
Kľúčové slová:
Korous theorem, orthogonal polynomials in two variables, weight function,
boundedness.
O článku:
J. Korous reached an important result for general orthogonal polynomials in one variable. He dealt with the boundedness and uniform boundedness of polynomials
$\bl\{Pn(x)\br\}n=0∞$
orthonormal with the weight function
$$ h(x)=δ (x)\widetilde{h}(x), $$
where $\widetilde{h}(x)$ is the weight function of another system of polynomials $\bl\{\widetilde{P}n(x)\br\}n=0∞$ orthonormal in the same interval and
$$ δ(x)≥ δ 0 >0 $$
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 $δ (x,y)$.
Ako citovať:
ISO 690:
Ftorek, B., Oršanský, P. 2014. Korous type inequalities for orthogonal polynomials in two variables. In Tatra Mountains Mathematical Publications, vol. 58, no.1, pp. 1-12. 1210-3195.
APA:
Ftorek, B., Oršanský, P. (2014). Korous type inequalities for orthogonal polynomials in two variables. Tatra Mountains Mathematical Publications, 58(1), 1-12. 1210-3195.