Bounds on the Segal-Bargmann Transform of L... Functions.
2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional derivatives,...
2000 Mathematics Subject Classification: 35A15, 44A15, 26A33The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.
Let be an analytic functional and let be the corresponding convolution operator on Sato’s space of hyperfunctions. We show that is surjective iff admits an elementary solution in iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are such that is not surjective on .