A.E. convergence of spectral sums on lie groups

Christopher Meaney; Detlef Müller; Elena Prestini

A.E. convergence of spectral sums on lie groups

Christopher Meaney^*, Detlef Müller, Elena Prestini

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let £ be a right-invariant sub-Laplacian on a connected Lie group G, and let S_Rf := f dE_λf, R ≥ O, denote the associated "spherical partial sums," where £ = ∫₀ ^∞ λ dE_λ is the spectral resolution of £. We prove that S_Rf(x) converges a.e. to f(x) as R → ∞ under the assumption log(2 + C) f ∞ L ² (G).

Original language	English
Pages (from-to)	1509-1520
Number of pages	12
Journal	Annales de l'Institut Fourier
Volume	57
Issue number	5
Publication status	Published - 2007

Cite this

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abstract = "Let £ be a right-invariant sub-Laplacian on a connected Lie group G, and let SRf := f dEλf, R ≥ O, denote the associated {"}spherical partial sums,{"} where £ = ∫0 ∞ λ dEλ is the spectral resolution of £. We prove that SRf(x) converges a.e. to f(x) as R → ∞ under the assumption log(2 + C) f ∞ L 2 (G).",

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T1 - A.E. convergence of spectral sums on lie groups

AU - Meaney, Christopher

AU - Müller, Detlef

AU - Prestini, Elena

PY - 2007

Y1 - 2007

N2 - Let £ be a right-invariant sub-Laplacian on a connected Lie group G, and let SRf := f dEλf, R ≥ O, denote the associated "spherical partial sums," where £ = ∫0 ∞ λ dEλ is the spectral resolution of £. We prove that SRf(x) converges a.e. to f(x) as R → ∞ under the assumption log(2 + C) f ∞ L 2 (G).

AB - Let £ be a right-invariant sub-Laplacian on a connected Lie group G, and let SRf := f dEλf, R ≥ O, denote the associated "spherical partial sums," where £ = ∫0 ∞ λ dEλ is the spectral resolution of £. We prove that SRf(x) converges a.e. to f(x) as R → ∞ under the assumption log(2 + C) f ∞ L 2 (G).

UR - https://www.scopus.com/pages/publications/36248953930

M3 - Article

AN - SCOPUS:36248953930

SN - 0373-0956

VL - 57

SP - 1509

EP - 1520

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 5

ER -

A.E. convergence of spectral sums on lie groups

Abstract

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