Displaying similar documents to “The Taylor transformation of analytic functionals with non-bounded carrier”

A Phragmén-Lindelöf type quasi-analyticity principle

Grzegorz Łysik (1997)

Studia Mathematica

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Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.

Asymptotic expansion of solutions of Laplace-Beltrami type singular operators

Maria Pliś (1995)

Studia Mathematica

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The theory of Mellin analytic functionals with unbounded carrier is developed. The generalized Mellin transform for such functionals is defined and applied to solve the Laplace-Beltrami type singular equations on a hyperbolic space. Then the asymptotic expansion of solutions is found.

The growth of entire solutions of differential equations of finite and infinite order

Lawrence Gruman (1972)

Annales de l'institut Fourier

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For certain Fréchet spaces of entire functions of several variables satisfying some specified growth conditions, we define a constant coefficient differential operator α ˇ as the transpose of a convolution operation in the dual space of continuous linear functionals and show that for f ( z ) in one of these spaces, their always exists a solution of the differential equation α ˇ ( x ) = f in the same space.