On the representation of smooth functions on the sphere using finitely many bits

DOI10.1016/j.acha.2004.11.004zbMath1082.41020OpenAlexW2002337104MaRDI QIDQ1780689

Hrushikesh N. Mhaskar

Publication date: 13 June 2005

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2004.11.004

zbMATH Keywords

metric entropypolynomial framesapproximation on the sphere

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Approximation by operators (in particular, by integral operators) (41A35) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

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Cites Work

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• On the representation of band limited functions using finitely many bits
• Polynomial operators and local smoothness classes on the unit interval
• Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order
• On the representation of band-dominant functions on the sphere using finitely many bits
• Entropy, universal coding, approximation, and bases properties
• Quantum approximation. II: Sobolev embeddings
• Tractability of approximation for weighted Korobov spaces on classical and quantum computers
• Weak convergence and empirical processes. With applications to statistics
• Approximation properties of zonal function networks using scattered data on the sphere
• Spherical harmonics
• Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen
• Unconditional bases and bit-level compression
• Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
• On the mathematical foundations of learning
• On simple oversampled A/D conversion in L/sup 2/(R)
• On the importance of combining wavelet-based nonlinear approximation with coding strategies
• Polynomial frames on the sphere

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