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Some remarks on convolution equations

C. A. Berenstein, M. A. Dostal (1973)

Annales de l'institut Fourier

Using a description of the topology of the spaces E ' ( Ω ) ( Ω open convex subset of R n ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution T , T E ' . We give applications to a class of distributions T satisfying cv. sing. supp. S * T = cv. sing. supp. S + cv. sing. supp. T for all S E ' .

Some results on the product of distributions and the change of variable

Emin Özçag, Brian Fisher (1991)

Commentationes Mathematicae Universitatis Carolinae

Let F and G be distributions in 𝒟 ' and let f be an infinitely differentiable function with f ' ( x ) > 0 , (or < 0 ). It is proved that if the neutrix product F G exists and equals H , then the neutrix product F ( f ) G ( f ) exists and equals H ( f ) .

Spaces of sequences, sampling theorem, and functions of exponential type

Rodolfo Torres (1991)

Studia Mathematica

We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called φ-transform studied in [6] [8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces.

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