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Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor, R. Meise, Dietmar Vogt (1990)

Annales de l'institut Fourier

Solving a problem of L. Schwartz, those constant coefficient partial differential operators P ( D ) are characterized that admit a continuous linear right inverse on ( Ω ) or 𝒟 ' ( Ω ) , Ω an open set in R n . For bounded Ω with C 1 -boundary these properties are equivalent to P ( D ) being very hyperbolic. For Ω = R n they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial P .

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.

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