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Commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1994)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the functions x r e - λ x and x s e + μ x is evaluated for r , s = 0 , 1 , 2 , ... and all λ , μ . Further commutative neutrix convolution products are then deduced.

Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

Banach Center Publications

Let L(z) be the Lie norm on ˜ = n + 1 and L*(z) the dual Lie norm. We denote by Δ ( B ˜ ( R ) ) the space of complex harmonic functions on the open Lie ball B ˜ ( R ) and by E x p Δ ( ˜ ; ( A , L * ) ) the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

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