Smoothness and Function Spaces Generated by Homogeneous Multipliers
Differential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin space...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/643135 |
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| _version_ | 1832559416897961984 |
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| author | Konstantin Runovski Hans-Jürgen Schmeisser |
| author_facet | Konstantin Runovski Hans-Jürgen Schmeisser |
| author_sort | Konstantin Runovski |
| collection | DOAJ |
| description | Differential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas for ψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed. |
| format | Article |
| id | doaj-art-5a4dabf5f7af4af5a17b2b4e8a682e43 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-5a4dabf5f7af4af5a17b2b4e8a682e432025-02-03T01:30:11ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/643135643135Smoothness and Function Spaces Generated by Homogeneous MultipliersKonstantin Runovski0Hans-Jürgen Schmeisser1Faculty of Mathematics and Informatics, Taurida National V. I. Vernadsky University, 95007 Simferopol, UkraineMathematical Institute, Friedrich-Schiller University Jena, 07737 Jena, GermanyDifferential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas for ψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.http://dx.doi.org/10.1155/2012/643135 |
| spellingShingle | Konstantin Runovski Hans-Jürgen Schmeisser Smoothness and Function Spaces Generated by Homogeneous Multipliers Journal of Function Spaces and Applications |
| title | Smoothness and Function Spaces Generated by Homogeneous Multipliers |
| title_full | Smoothness and Function Spaces Generated by Homogeneous Multipliers |
| title_fullStr | Smoothness and Function Spaces Generated by Homogeneous Multipliers |
| title_full_unstemmed | Smoothness and Function Spaces Generated by Homogeneous Multipliers |
| title_short | Smoothness and Function Spaces Generated by Homogeneous Multipliers |
| title_sort | smoothness and function spaces generated by homogeneous multipliers |
| url | http://dx.doi.org/10.1155/2012/643135 |
| work_keys_str_mv | AT konstantinrunovski smoothnessandfunctionspacesgeneratedbyhomogeneousmultipliers AT hansjurgenschmeisser smoothnessandfunctionspacesgeneratedbyhomogeneousmultipliers |