The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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

Similarity:

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.