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  • We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator D such that the localization operator with symbol f coincides with the Toeplitz operator with symbol Df. An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Coburn and simplifies and generalizes recent results of Lo.
  • We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator D such that the localization operator with symbol f coincides with the Toeplitz operator with symbol Df. An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Coburn and simplifies and generalizes recent results of Lo. (en)
  • Práce dokazuje, že pro každý lokalizační operátor na Fockově prostoru s polynomiálním oknem existuje lineární diferenciální operátor D takový, že lokalizační operátor se symbolem f se rovná Toeplitzovu operátoru se symbolem Df. Podobný výsledek je dokázán i pro standardní Bergmanovy prostory na omezených symetrických oblastech. Tím je ověřena nedávná hypotéza L. Coburna a zjednodušen nedávný výsledek M.-L. Lo. (cs)
Title
  • Toeplitz operators and localization operators
  • Toeplitz operators and localization operators (en)
  • Toeplitzovy operátory a lokalizační operátory (cs)
skos:prefLabel
  • Toeplitz operators and localization operators
  • Toeplitz operators and localization operators (en)
  • Toeplitzovy operátory a lokalizační operátory (cs)
skos:notation
  • RIV/67985840:_____/09:00321306!RIV09-AV0-67985840
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  • P(GA201/06/0128), Z(AV0Z10190503)
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  • RIV/67985840:_____/09:00321306
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  • Toeplitz operator; localization operator; Bergman space (en)
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  • US - Spojené státy americké
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  • [E09EA7A084FC]
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  • American Mathematical Society. Transactions
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  • 361
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  • Engliš, Miroslav
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  • 000261255300002
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  • 0002-9947
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