Duality and approximation of Bergman spaces
| Autor: | Debraj Chakrabarti, Luke D. Edholm, J. D. McNeal |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Mathematics - Complex Variables Mathematics::Complex Variables General Mathematics Laurent series 010102 general mathematics Hardy space 01 natural sciences symbols.namesake Operator (computer programming) Norm (mathematics) Bounded function 0103 physical sciences symbols FOS: Mathematics 010307 mathematical physics 0101 mathematics Complex Variables (math.CV) 32A36 32A25 32C37 32E30 32W05 Reinhardt domain Mathematics |
| DOI: | 10.48550/arxiv.1804.02746 |
| Popis: | Expected duality and approximation properties are shown to fail on Bergman spaces of domains in C n , via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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