caa a22 4500 445836962 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00209-010-0711-8 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0711-8 Sontz Stephen Centro de Investigación en Matemáticas, A.C. (CIMAT), Guanajuato, Mexico aut On Segal-Bargmann analysis for finite Coxeter groups and its heat kernel [Elektronische Daten] [Stephen Sontz] We prove identities involving the integral kernels of three versions (two being introduced here) of the Segal-Bargmann transform associated to a finite Coxeter group acting on a finite dimensional, real Euclidean space (the first version essentially having been introduced around the same time by Ben Saïd and Ørsted and independently by Soltani) and the Dunkl heat kernel, due to Rösler, of the Dunkl Laplacian associated with the same Coxeter group. All but one of our relations are originally due to Hall in the context of standard Segal-Bargmann analysis on Euclidean space. Hall's results (trivial Dunkl structure and arbitrary finite dimension) as well as our own results inμ-deformed quantum mechanics (non-trivial Dunkl structure, dimension one) are particular cases of the results proved here. So we can understand all of these versions of the Segal-Bargmann transform associated to a Coxeter group as Hall type transforms. In particular, we define an analogue of Hall's Version C generalized Segal-Bargmann transform which is then shown to be Dunkl convolution with the Dunkl heat kernel followed by analytic continuation. In the context of Version C we also introduce a new Segal-Bargmann space and a new transform associated to the Dunkl theory. Also we have what appears to be a new relation in this context between the Segal-Bargmann kernels for Versions A and C. Springer-Verlag, 2010 Segal-Bargmann analysis nationallicence Heat kernel analysis nationallicence Coxeter group nationallicence Dunkl operator nationallicence Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 9-28 0025-5874 269:1-2<9 2011 269 209 https://doi.org/10.1007/s00209-010-0711-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0711-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sontz Stephen Centro de Investigación en Matemáticas, A.C. (CIMAT), Guanajuato, Mexico aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 9-28 0025-5874 269:1-2<9 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer