Let X be a rearrangement-invariant space of Lebesgue-measurable functions on , such as the classical Lebesgue, Lorentz or Orlicz spaces. Given a nonnegative, measurable (weight) function on , define . We investigate conditions on such a weight w that guarantee X(w) is an algebra under the convolution product F∗G defined at by ; more precisely, when for all F,G ∈ X(w).
A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.
Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution of measures...