Displaying similar documents to “Liouville type theorem for solutions of linear partial differential equations with constant coefficients”

Integro-differential-difference equations associated with the Dunkl operator and entire functions

Néjib Ben Salem, Samir Kallel (2004)

Commentationes Mathematicae Universitatis Carolinae

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In this work we consider the Dunkl operator on the complex plane, defined by 𝒟 k f ( z ) = d d z f ( z ) + k f ( z ) - f ( - z ) z , k ≥ 0 . We define a convolution product associated with 𝒟 k denoted * k and we study the integro-differential-difference equations of the type μ * k f = ∑ n = 0 ∞ a n , k 𝒟 k n f , where ( a n , k ) is a sequence of complex numbers and μ is a measure over the real line. We show that many of these equations provide representations for particular classes of entire functions of exponential type.

On a space of entire functions rapidly decreasing on Rn and its Fourier transform

Il’dar Kh. Musin (2015)

Concrete Operators

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A space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained.