Algorithm for construction of quadrature formulas with exponential convergence for linear operators acting on periodic functions

2021 ◽  
pp. 86-92
Author(s):  
Alexander Georgievich Petrov ◽  
Keyword(s):  
Exponential Convergence ◽  
Linear Operators ◽  
Quadrature Formulas ◽  
Periodic Functions

scholarly journals The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Joachim Toft
Keyword(s):  
Operator Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Modulation Spaces ◽  
Zak Transform ◽  
Periodic Functions ◽  
Distribution Spaces ◽  
Necessary And Sufficient

AbstractWe characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operators in order for these operators should be conjugations by Zak transforms.

scholarly journals Positive linear operators and the approximation of continuous functions on locally compact abelian groups

1980 ◽  
Vol 30 (2) ◽  
pp. 180-186 ◽  
Author(s):  
Walter R. Bloom ◽  
Joseph F. Sussich
Keyword(s):  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Locally Compact Abelian Group ◽  
Periodic Functions ◽  
Locally Compact ◽  
Character Group ◽  
Spaces Of Continuous Functions ◽  
Compact Abelian Groups ◽  
Approximation Of Continuous Functions

AbstractIn 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2π-periodic functions and limn→rTnf = f uniformly for f = 1, cos and sin. then limn→rTnf = f uniformly for all f∈C. We extend this result to spaces of continuous functions defined on a locally compact abelian group G, with the test family {1, cos, sin} replaced by a set of generators of the character group of G.

scholarly journals The degree of approximation by positive operators on compact connected abelian groups

1982 ◽  
Vol 33 (3) ◽  
pp. 364-373 ◽  
Author(s):  
Walter R. Bloom ◽  
Joseph F. Sussich
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Abelian Groups ◽  
Degree Of Approximation ◽  
Linear Operators ◽  
Test Functions ◽  
Periodic Functions ◽  
Quantitative Version ◽  
Approximation By Positive Operators ◽  
Korovkin’S Theorem

AbstractIn 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2 π-periodic functions and lim Tnf = f uniformly for f = 1, cos and sin, then lim Tnf = f uniformly for all f ∈ C. Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of f. We extend this result by giving a quantitative version of Korovkin's theorem for compact connected abelian groups.

scholarly journals A Korovkin Type Approximation Theorem and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Malik Saad Al-Muhja
Keyword(s):  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Stieltjes Integral ◽  
Periodic Functions ◽  
Third Order ◽  
Korovkin Type Approximation Theorem ◽  
The Third ◽  
Type Approximation ◽  
Statistical Limit

We present a Korovkin type approximation theorem for a sequence of positive linear operators defined on the space of all real valued continuous and periodic functions viaA-statistical approximation, for the rate of the third order Ditzian-Totik modulus of smoothness. Finally, we obtain an interleave between Riesz's representation theory and Lebesgue-Stieltjes integral-i, for Riesz's functional supremum formula via statistical limit.

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