Parseval Space-Frequency Localized Frames on Sub-Riemannian Compact Homogeneous Manifolds

DOI10.1007/978-3-319-55550-8_17zbMath1385.42029arXiv1612.05755OpenAlexW2593266172MaRDI QIDQ4609738

Isaac Z. Pesenson

Publication date: 26 March 2018

Published in: Frames and Other Bases in Abstract and Function Spaces (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.05755

zbMATH Keywords

sub-Riemannian manifoldParseval framenon-isotropic Sobolev spacecompact homogeneous manifoldnon-isotropic Besov spacesub-elliptic Laplace operatorsub-elliptic positive cubature formula

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Harmonic analysis on homogeneous spaces (43A85) General harmonic expansions, frames (42C15)

Related Items (4)

A Plancherel-Polya inequality in Besov spaces on spaces of homogeneous type ⋮ From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere ⋮ Geometric space-frequency analysis on manifolds ⋮ Parseval wavelet frames on Riemannian manifold

Cites Work

• Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds
• Theory of function spaces II
• Balls and metrics defined by vector fields. I: Basic properties
• Hypoelliptic differential operators and nilpotent groups
• Estimations of the heat kernel on homogeneous spaces
• Poincaré-type inequalities and reconstruction of Paley-Wiener functions on manifolds
• Heat kernel generated frames in the setting of Dirichlet spaces
• A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
• Bernstein-Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds
• Hypoelliptic second order differential equations
• Functions which are smooth along vector fields
• Kolmogorov and Linear Widths of Balls in Sobolev Spaces on Compact Manifolds
• A sampling theorem on homogeneous manifolds
• Cubature Formulas and Discrete Fourier Transform on Compact Manifolds
• A Class of Nonharmonic Fourier Series
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