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Integral representation of superoscillations via complex Borel measures and their convergence.
- Source :
-
Transactions of the American Mathematical Society . Sep2023, Vol. 376 Issue 9, p6315-6340. 26p. - Publication Year :
- 2023
-
Abstract
- In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some convergence to a plane wave is the standard characterizing feature of a superoscillating function in mathematics and quantum mechanics. Also there exists a certain discrepancy between the representation of superoscillations either as generalized Fourier series, as certain integrals or via special functions. The aim of this work is to close these gaps and give a general definition of superoscillations, covering the well-known examples in the existing literature. Superoscillations will be defined as sequences of holomorphic functions, which admit integral representations with respect to complex Borel measures and converge to a plane wave in the space \mathcal {A}_1(\mathbb {C}) of entire functions of exponential type. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 376
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 170039176
- Full Text :
- https://doi.org/10.1090/tran/8983