Imaginary Powers of the Dunkl Harmonic Oscillator
In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on Rd isomorphic to Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1 into weak L^1.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2009-02-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.016 |
| _version_ | 1819038783259017216 |
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| author | Adam Nowak Krzysztof Stempak |
| author_facet | Adam Nowak Krzysztof Stempak |
| author_sort | Adam Nowak |
| collection | DOAJ |
| description | In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on Rd isomorphic to Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1 into weak L^1. |
| first_indexed | 2024-12-21T08:42:48Z |
| format | Article |
| id | doaj.art-2a494b12464f446eb64a85c7e1bf2694 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-21T08:42:48Z |
| publishDate | 2009-02-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-2a494b12464f446eb64a85c7e1bf26942022-12-21T19:09:54ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-02-015016Imaginary Powers of the Dunkl Harmonic OscillatorAdam NowakKrzysztof StempakIn this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on Rd isomorphic to Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1 into weak L^1.http://dx.doi.org/10.3842/SIGMA.2009.016Dunkl operatorsDunkl harmonic oscillatorimaginary powersCalderón-Zygmund operators |
| spellingShingle | Adam Nowak Krzysztof Stempak Imaginary Powers of the Dunkl Harmonic Oscillator Symmetry, Integrability and Geometry: Methods and Applications Dunkl operators Dunkl harmonic oscillator imaginary powers Calderón-Zygmund operators |
| title | Imaginary Powers of the Dunkl Harmonic Oscillator |
| title_full | Imaginary Powers of the Dunkl Harmonic Oscillator |
| title_fullStr | Imaginary Powers of the Dunkl Harmonic Oscillator |
| title_full_unstemmed | Imaginary Powers of the Dunkl Harmonic Oscillator |
| title_short | Imaginary Powers of the Dunkl Harmonic Oscillator |
| title_sort | imaginary powers of the dunkl harmonic oscillator |
| topic | Dunkl operators Dunkl harmonic oscillator imaginary powers Calderón-Zygmund operators |
| url | http://dx.doi.org/10.3842/SIGMA.2009.016 |
| work_keys_str_mv | AT adamnowak imaginarypowersofthedunklharmonicoscillator AT krzysztofstempak imaginarypowersofthedunklharmonicoscillator |