Eigenvalue decay of positive integral operators on the sphere
نویسندگان
چکیده
منابع مشابه
Jackson Kernels: a Tool for Analysing the Decay of Eigenvalue Sequences of Integral Operators on the Sphere
Decay rates for the sequence of eigenvalues of positive and compact integral operators have been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square integrable functions on the unit sphere and generated by a kernel satisfying a Hölder type assumption defined by average operators. In the approach to be presented...
متن کاملApproximation numbers of integral operators on the sphere
This work derives sharp estimates for approximation numbers of positive integral operators on the sphere when the generating kernel satisfies an abstract Hölder condition defined by spherical convolutions with uniformly bounded bi-zonal kernels. The estimates are obtained via finite rank operators defined by both, certain generalized Jackson kernels and the operators appearing in the Hölder con...
متن کاملSingular Integral Operators and Essential Commutativity on the Sphere
Let T be the C∗-algebra generated by the Toeplitz operators {Tφ : φ ∈ L∞(S, dσ)} on the Hardy space H(S) of the unit sphere in C. It is well known that T is contained in the essential commutant of {Tφ : φ ∈ VMO∩L∞(S, dσ)}. We show that the essential commutant of {Tφ : φ ∈ VMO∩L∞(S, dσ)} is strictly larger than T .
متن کاملEigenvalue Decay of Operators on Harmonic Function Spaces
Let Ω be an open set in R (d > 1) and h(Ω) the Fréchet space of harmonic functions on Ω. Given a bounded linear operator L : h(Ω) → h(Ω), we show that its eigenvalues λn, arranged in decreasing order and counting multiplicities, satisfy |λn| ≤ K exp(−cn ), where K and c are two explicitly computable positive constants.
متن کاملEigenvalue Decay of Integral Operators Generated by Power Series–like Kernels
We deduce decay rates for eigenvalues of integral operators generated by power serieslike kernels on a subset X of either Rq or Cq . A power series-like kernel is a Mercer kernel having a series expansion based on an orthogonal family { fα}α∈Zq+ in L 2(X ,μ) , in which μ is a complete measure on X . As so, we show that the eigenvalues of the integral operators are given by an explicit formula d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02595-6