Displaying similar documents to “Spectral Riesz-Cesàro means: How the square root function helps us to see around the world.”

Asymptotic analysis of non-self-adjoint Hill operators

Oktay Veliev (2013)

Open Mathematics

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We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically...

An answer to a question of Cao, Reilly and Xiong

Zafer Ercan, S. Onal (2006)

Czechoslovak Mathematical Journal

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We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.

Convolution of radius functions on ℝ³

Konstanty Holly (1994)

Annales Polonici Mathematici

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We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in...