On the approximation by generalized sampling series in Lp - Metrics

Sampling Theory in Signal and Image Processing

Volumn 5, Issue 1, 2006, Pages 59-87

  Burinska, Z ^a   Runovski, K ^a   Schmeisser, H J ^b  

^a INTERREGIONAL ACADEMY OF PERSONNEL MANAGEMENT   (Ukraine)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Convolution integrals; Fej r and de La Valle Poussin kernels; Fourier transform; Generalized sampling series and their families; K functionals and their realizations; Riesz derivative

Indexed keywords

EID: 33646567774     PISSN: 15306429     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
2. Z. Burinska, Methods of Trigonometric and Sampling Approximation, Thesis, Friedrich-Schiller-University Jena, 2003.
3. Z. Burinska, K. Runovski and H.-J. Schmeisser, On the method of approximation by families of linear polynomial operators, Z. Anal. Anwend., 19, 677-693, 2000.
4. P.L. Butzer and R. Nessel, Fourier Analysis and Approximation, Academic Press, New-York and London, 1971.
5. P.L. Butzer, G. Schmeisser and R.L. Stens, An Introduction to Sampling Analysis, In Sampling in Theory and Practice, Kluwer Academic/Plenum Publishers, New York, 2000.
6. P.L. Butzer, W. Splettstösser and R. L. Stens, The sampling theorem and linear prediction in signal analysis, Jahresber. Dtsch. Math.-Ver., 90, 1-70, 1988.
7. R. DeVore and G. Lorentz: Constructive Approximation, Springer Verlag, Berlin, 1993.
8. p, 0 < p < 1, Constr. Approx., 11, 67-83, 1995.
9. Z. Ditzian, and K. Ivanov, Strong converse inequalities, J. Anal. Math., 61, 61-111, 1993.
10. Z. Ditzian K. Runovski, Realization and smoothness related to the Laplacian, Acta Math. Hungar., 93, 189-223, 2001.,
11. J.R. Higgins, Sampling Theory in Fourier and Signal Analysis. Foundations, Clarendon Press, Oxford, 1996.
12. L. Hörmander, The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis, Springer Verlag, Berlin, 1983.
13. V. Hristov and K. Ivanov, Realization of K-functionals on subsets and constrained approximation, Math. Balkanica, 4, 236-257, 1990.
14. S.M. Nikolskij, Approximation of Functions of Several Variables and Embedding Theorems, Nauka, Moskva, 1969. (Russian) Springer Verlag, Berlin, 1975. (English translation)
15. M. Plancherel and C. Polya, Fonctions entieres et integrales de Fourier multiples. I, II, Comment. Math. Helvetici, 9, 224-248, 1937 and 10, 110-163, 1938.
16. p-spaces, 0 < p < 1, Mat. Sb., 78, 165-173, 1994. (Russian) Sbornik: Mathematics, 184, 33-42, 1993. (English translation)
17. p-spaces, 0 < p < 1, Mat. Sb., 82, 441-459, 1995. (Russian) Sbornik: Mathematics, 185, 81-102, 1994. (English translation)
18. K. Runovski, On Approximation by Families of Linear Polynomial Operators, Habilitation Thesis, Friedrich-Schiller-University Jena, 1995.
19. H.-J. Schmeisser and W. Sickel, Sampling Theory and Function Spaces, In Applied Mathematics Reviews. Vol. 1, World Scientific, Singapore, New Jersey, London, Hong Kong, 2000.
20. R.L. Stens, Sampling by generalized kernels, In Sampling Theory in Fourier and Signal Analysis. Advanced Topics, University Press, Oxford 1999.
21. p-spaces, 0 < p < 1, Mat. Sb., 98, 395-415, 1975. (Russian)
22. A.F. Timan, Theory of Approximation of Functions of a Real Variable, Dover Publ. Inc, New York, 1994.
23. H. Triebel, Higher Analysis, Johann Ambrosius Barth, Leipzig-Berlin-Heidelberg, 1992.
24. H. Triebel, Theory of Function Spaces, Geest&Portig K.-G., Leipzig, 1983.