Displaying similar documents to “Wiener type theorem for regular operators of bounded support”

Liouville type theorem for solutions of linear partial differential equations with constant coefficients

Akira Kaneko (2000)

Annales Polonici Mathematici

Similarity:

We discuss existence of global solutions of moderate growth to a linear partial differential equation with constant coefficients whose total symbol P(ξ) has the origin as its only real zero. It is well known that for such equations, global solutions tempered in the sense of Schwartz reduce to polynomials. This is a generalization of the classical Liouville theorem in the theory of functions. In our former work we showed that for infra-exponential growth the corresponding assertion is...

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.