Open Access

Korous Type Inequalities for Orthogonal Polynomials in two Variables

Tatra Mountains Mathematical Publications's Cover Image
Tatra Mountains Mathematical Publications
Real Functions ‘13 Real Functions, Topology, Real and Functional Analysis, Locally Convex Spaces

Cite

[1] DUNHAM, J.: Fourier Series and Orthogonal Polynomials. Dover Publications, Mineola, NY, 2004.Search in Google Scholar

[2] DUNKL, CH. F.-XU, Y.: Orthogonal Polynomials of Several Variables, in: Encyclopedia Math. Appl., Vol. 81, Cambridge Univ. Press, Cambridge, 2001.10.1017/CBO9780511565717Search in Google Scholar

[3] JACKSON, D.: Fourier Series and Orthogonal Polynomials. Carus Math. Monogr., Vol. VI, Math. Assoc. America, Washington, DC, 1941.Search in Google Scholar

[4] KOORNWINDER, T. H.: Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators I, II, Indag. Math. 36 (1974), 48-66.10.1016/1385-7258(74)90013-4Search in Google Scholar

[5] KOORNWINDER, T. H.: Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators III, IV, Indag. Math. 36 (1974), 357-381.10.1016/1385-7258(74)90026-2Search in Google Scholar

[6] KOROUS, J.: On the development of functions of one real variable in the certain series of orthogonal polynomials, Rozpravy II. třidy České akademie věd v Praze 40 (1938), 1-12. (In Czech)Search in Google Scholar

[7] KRALL, H. L.-SHEFFER, I. M.: Orthogonal polynomials in two variables, Ann. Mat. Pura Appl. (4) 76 (1967), 325-376.10.1007/BF02412238Search in Google Scholar

[8] MARČOKOVÀ, M.: Second order partial differential equations for some orthogonal polynomials in two variables, Stud. Univ. ˇ Zilina Math. Phys. Ser. 13 (2001), 127-132.Search in Google Scholar

[9] MARČOKOVÀ, M.: Approximation of functions in two variables by Ces`aro means of Fourier-Jacobi sums, in: Proc. of the Internat. Scientific Conf. of Mathematics, Vol. 1, (P. Marušiak et al., eds.), Žilina, Slovakia, 1998, EDIS, Žilina University Publisher, Žilina, 1999, pp. 161-165.Search in Google Scholar

[10] MARČOKOVÀ, M.-GULDAN, V.: On one orthogonal transform applied on a system of orthogonal polynomials in two variables, J. Appl. Math.-Aplimat 2 (2009), pp. 239-245.Search in Google Scholar

[11] SUETIN, P. K.: Orthogonal Polynomials in Two Variables, in: Anal. Methods Spec. Funct., Vol. 3, Gordon and Breach Sci. Publ., Amsterdam, 1999.Search in Google Scholar

[12] SZABŁLOWSKI, P. J.: On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures, Appl. Math. Comput. 219 (2013), 6768-6776.Search in Google Scholar

[13] SZEGÖ, B.: Orthogonal Polynomials. Nauka, Moscow, 1962. (In Russian) Search in Google Scholar

eISSN:
1210-3195
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics