Strong summability of orthogonal expansions of summable functions. II

1996 ◽  
Vol 48 (3) ◽  
pp. 438-452
Author(s):  
A. I. Stepanets ◽  
R. A. Lasuriya
Keyword(s):  
Strong Summability ◽  
Orthogonal Expansions

Strong summability of orthogonal expansions of summable functions. I

1996 ◽  
Vol 48 (2) ◽  
pp. 294-313
Author(s):  
A. I. Stepanets ◽  
R. A. Lasuriya
Keyword(s):  
Strong Summability ◽  
Orthogonal Expansions

On the rate of pointwise strong summability of orthogonal expansions

2007 ◽  
Vol 56 (2) ◽  
pp. 273-286
Author(s):  
Włodzimierz Łenski ◽  
Radosława Kranz
Keyword(s):  
Strong Summability ◽  
Orthogonal Expansions

Points of strong summability of conjugate series of Fourier series

1984 ◽  
Vol 36 (5) ◽  
pp. 828-834
Author(s):  
O. D. Gabisoniya
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Conjugate Series

Some theorems on strong summability

1965 ◽  
Vol 90 (4) ◽  
pp. 310-318 ◽  
Author(s):  
Babban Prasad Mishra
Keyword(s):  
Strong Summability

scholarly journals Orthogonal structure on a quadratic curve

2020 ◽  
Author(s):  
Sheehan Olver ◽  
Yuan Xu
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Extension Problem ◽  
Orthogonal Expansions ◽  
Schrödinger’S Equation ◽  
Fourier Extension ◽  
Quadratic Curve ◽  
Interpolation Of Functions ◽  
Fourier Orthogonal Expansions ◽  
Schrödinger's Equation

Abstract Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.

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