Entropy and Widths of Multiplier Operators on Two-Point Homogeneous Spaces

Kushpel, Alexander; Tozoni, Sérgio Antonio

doi:10.1007/s00365-011-9146-7

Cited by 32 publications

(39 citation statements)

References 22 publications

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“…These spaces are manifolds having an invariant Riemannian (geodesic) metric and can be endowed with a measure that permits to consider the Laplace-Beltrami operator on it, which can be used in order to define the smootheness condition in the same way we did here. We suggest [BrDa05,KuTo12] and references therein for more detailed information about these spaces.…”

Section: Resultsmentioning

confidence: 99%

Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere

Castro

Jordão²,

Peron³

2020

Journal of Computational and Applied Mathematics

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This paper brings results about the behavior of sequences of eigenvalues or singular values of integral operators generated by square-integrable kernels on the real m-dimensional unit sphere, m ≥ 2. Under smoothness assumptions on the kernels, given via (infinitely many times) Laplace-Beltrami differentiability, we obtain super-exponential decay rates for the eigenvalues of positive integral operators and for singular values of those which are non-positive. The positive case is shown to be optimal. We also provide a list of parametric families of these kernels, which are of interest for numerical analysis and geostatistical communities.MSC: 45C05 (41A36 42A82 45M05 45P05 47A75)

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Section: Resultsmentioning

confidence: 99%

Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere

Castro

Jordão²,

Peron³

2020

Journal of Computational and Applied Mathematics

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“…The next result present a relation between integrals in L 2 (M d ) and L α,β 1 ([−1, 1]) and can be found in the references [3], [11], [15].…”

Section: A Appendix: a Proof For The Funk-hecke Formulamentioning

confidence: 99%

“…In general this classification is decisive in analysis of problems involving the compact two‐point homogeneous spaces, as can be seen in –, , .…”

Section: Introductionmentioning

confidence: 99%

“…. ; (v) The Cayley projective plane P d (Cay), d = 16.In general this classification is decisive in analysis of problems involving the compact two-point homogeneous spaces, as can be seen in [1]-[3], [7], [15].The continuity of a function K : M d × M d → R can be defined through the usual Riemannian (geodesic) distance on M d , here assumed to be normalized so that all geodesics on M d have the same length 2π . The distance between two points x, y ∈ M d will be denoted by |x y|.…”

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Covering numbers of isotropic reproducing kernels on compact two‐point homogeneous spaces

Azevedo

Barbosa²

2017

Mathematische Nachrichten

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In this paper we present upper and lower estimates for the covering numbers of the unit ball of a reproducing kernel Hilbert space associated to a continuous isotropic kernel on a compact two‐point homogeneous space (CTPHS). These estimates are obtained from estimates on the decay of the Fourier–Jacobi coefficients of the kernel via applications of the Funk–Hecke formula and the Schoenberg series representation of an isotropic kernel on CTPHS and also by the use of cubature formulas on these spaces.

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“…Os elementos da base S d k,a são comumente chamados de harmônicos esféricos. Mais informações sobre a Fórmula de Adição, sua aplicabilidade e sobre a análise harmônica em geral atrelada aos espaços M d podem ser encontradas em [8,9,28,36] e nas referências lá citadas.…”

Section: -Homogêneosunclassified

Núcleos isotrópicos e positivos definidos sobre espaços 2-homogêneos

Bonfim¹

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Entropy and Widths of Multiplier Operators on Two-Point Homogeneous Spaces

Cited by 32 publications

References 22 publications

Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere

Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere

Covering numbers of isotropic reproducing kernels on compact two‐point homogeneous spaces

Núcleos isotrópicos e positivos definidos sobre espaços 2-homogêneos

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