Displaying similar documents to “Characterizing weakly symmetric spaces as Gelfand pairs.”

On nowhere weakly symmetric functions and functions with two-element range

Krzysztof Ciesielski, Kandasamy Muthuvel, Andrzej Nowik (2001)

Fundamenta Mathematicae

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A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each...

On the symmetric continuity

Jaskuła, Janusz, Szkopińska, Bożena (2015-12-15T14:49:03Z)

Acta Universitatis Lodziensis. Folia Mathematica

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Polynomially growing pluriharmonic functions on Siegel domains

Monika Gilżyńska (2007)

Colloquium Mathematicae

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Let 𝓓 be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let N(Φ)S be a solvable Lie group acting simply transitively on 𝓓. We characterize polynomially growing pluriharmonic functions on 𝓓 by means of three N(Φ)S-invariant second order elliptic degenerate operators.

Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

T. Alvarez, R. Cross, A. Gouveia (1995)

Studia Mathematica

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Characterisations are obtained for the following classes of unbounded linear operators between normed spaces: weakly compact, weakly completely continuous, and unconditionally converging operators. Examples of closed unbounded operators belonging to these classes are exhibited. A sufficient condition is obtained for the weak compactness of T' to imply that of T.