Beyond superoscillation: general theory of approximation with bandlimited functions

DOI10.1088/1751-8121/ad09ecarXiv2306.03963MaRDI QIDQ6148234

Andrew N. Jordan, Tathagata Karmakar

Publication date: 11 January 2024

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.03963

zbMATH Keywords

approximationLegendre polynomialssuperresolutionspherical Bessel functionsbandlimitedsuperoscillationsupergrowth

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Quantum optics (81V80) Approximation by polynomials (41A10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (32A37) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Special quantum systems, such as solvable systems (81Q80) Quantum control (81Q93)

Cites Work

• Unnamed Item
• Four aspects of superoscillations
• Black holes, bandwidths and Beethoven
• Scaling properties of superoscillations and the extension to periodic signals
• New methods for creating superoscillations
• Superoscillations: Faster Than the Nyquist Rate
• Superoscillations with arbitrary polynomial shape
• Construction of Aharonov–Berry's superoscillations
• Evolution of quantum superoscillations and optical superresolution without evanescent waves

This page was built for publication: Beyond superoscillation: general theory of approximation with bandlimited functions