Quantum Harmonic Analysis for Polyanalytic Fock Spaces
We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in recent work by the second author and answer a few related open questions. For instance, we show that there exists a sym...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2024-12, Vol.30 (6), Article 63 |
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| creator | Fulsche, Robert Hagger, Raffael |
| description | We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in recent work by the second author and answer a few related open questions. For instance, we show that there exists a symbol such that the corresponding Toeplitz operator is unitary on the analytic Fock space but vanishes completely on one of the true polyanalytic Fock spaces. This follows directly from an explicit characterization of the kernel of the Toeplitz quantization, which we derive using quantum harmonic analysis. Moreover, we show that the Berezin transform is injective on the set of of Toeplitz operators. Finally, we provide several characterizations of the
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1
-algebra in terms of integral kernel estimates and essential commutants. |
| doi_str_mv | 10.1007/s00041-024-10124-9 |
| format | Article |
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C
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C
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-algebra in terms of integral kernel estimates and essential commutants.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Fourier Analysis</subject><subject>Harmonic analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Partial Differential Equations</subject><subject>Signal,Image and Speech Processing</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9UMFOwzAMjRBIjMEPcKrEuWDHaZoep4kxpEmAgHOUpina2JqRtIf9PRlF4sbFtuz3np8eY9cItwhQ3kUAEJgDFzkCplqdsAkWhHmhCjxNM8gqzbI6ZxcxbgA4UkkTJl8G0_XDLluasPPd2mazzmwPcR2z1ofs2W8P5rjo02Xh7Wf2ujfWxUt21pptdFe_fcreF_dv82W-enp4nM9WueVC9LkoualBKmdbhQpLkoJqVUnBLSavDapatVRJJ62UBE2NiBwLJVzbkKhLmrKbUXcf_NfgYq83fgjJUNSEnEgCSp5QfETZ4GMMrtX7sN6ZcNAI-piPHvPR6af-yUdXiUQjKSZw9-HCn_Q_rG_FW2W6</recordid><startdate>20241201</startdate><enddate>20241201</enddate><creator>Fulsche, Robert</creator><creator>Hagger, Raffael</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4289-3025</orcidid><orcidid>https://orcid.org/0000-0003-3218-9410</orcidid></search><sort><creationdate>20241201</creationdate><title>Quantum Harmonic Analysis for Polyanalytic Fock Spaces</title><author>Fulsche, Robert ; Hagger, Raffael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-472ab068ecf818173643b89642c1024d18b8f396e6c6630db11121584efd34b73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Fourier Analysis</topic><topic>Harmonic analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Partial Differential Equations</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fulsche, Robert</creatorcontrib><creatorcontrib>Hagger, Raffael</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fulsche, Robert</au><au>Hagger, Raffael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum Harmonic Analysis for Polyanalytic Fock Spaces</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2024-12-01</date><risdate>2024</risdate><volume>30</volume><issue>6</issue><artnum>63</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in recent work by the second author and answer a few related open questions. For instance, we show that there exists a symbol such that the corresponding Toeplitz operator is unitary on the analytic Fock space but vanishes completely on one of the true polyanalytic Fock spaces. This follows directly from an explicit characterization of the kernel of the Toeplitz quantization, which we derive using quantum harmonic analysis. Moreover, we show that the Berezin transform is injective on the set of of Toeplitz operators. Finally, we provide several characterizations of the
C
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-algebra in terms of integral kernel estimates and essential commutants.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-024-10124-9</doi><orcidid>https://orcid.org/0000-0002-4289-3025</orcidid><orcidid>https://orcid.org/0000-0003-3218-9410</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Harmonic analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Operators (mathematics) Partial Differential Equations Signal,Image and Speech Processing |
| title | Quantum Harmonic Analysis for Polyanalytic Fock Spaces |
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