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Periodic Boehmians.

Nemzer, Dennis (1989)

International Journal of Mathematics and Mathematical Sciences

Poincaré theorem and nonlinear PDE's

Maria E. Pliś (1998)

Annales Polonici Mathematici

A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these distributions are locally finite.

Pointwise Fourier inversion of distributions on spheres

Francisco Javier González Vieli (2017)

Czechoslovak Mathematical Journal

Given a distribution T on the sphere we define, in analogy to the work of Łojasiewicz, the value of T at a point ξ of the sphere and we show that if T has the value τ at ξ , then the Fourier-Laplace series of T at ξ is Abel-summable to τ .

Polynomial ultradistributions: differentiation and Laplace transformation

O. Łopuszański (2010)

Banach Center Publications

We consider the multiplicative algebra P(𝒢₊') of continuous scalar polynomials on the space 𝒢₊' of Roumieu ultradistributions on [0,∞) as well as its strong dual P'(𝒢₊'). The algebra P(𝒢₊') is densely embedded into P'(𝒢₊') and the operation of multiplication possesses a unique extension to P'(𝒢₊'), that is, P'(𝒢₊') is also an algebra. The operation of differentiation on these algebras is investigated. The polynomially extended Laplace transformation and its connections with the differentiation...

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