TY - JOUR
ID - 65772
T1 - Operators of Laplace transform type and a new class of hypergeometric coefficients
JO - Advances in Operator Theory
JA - AOT
LA - en
SN -
A1 - Bond, Stuart
A1 - Taheri, Ali
Y1 - 2019
PY - 2019/01/01
VL - 4
IS - 1
SP - 226
EP - 250
KW - Schwartz kernel
KW - operator of Laplace transform type
KW - Laplace-Beltrami operator
KW - hypergeometric function
KW - Maclaurin spectral function
KW - symmetric space
DO - 10.15352/aot.1804-1356
N2 - A differential identity on the hypergeometric function ${}_2F_1(a,b;c;z)$ unifying and extending certain spectral results on the scale of Gegenbauer and Jacobi polynomials and leading to a new class of hypergeometric related scalars $mathsf{c}_j^m(a,b,c)$ and polynomials $mathscr{R}_m=mathscr{R}_m(X)$ is established. The Laplace-Beltrami operator on a compact rank one symmetric space is considered next and for operators of the Laplace transform type by invoking an operator trace relation, the Maclaurin spectral coefficients of their Schwartz kernel are fully described. Other representations as well as extensions of the differential identity to the generalised hypergeometric function ${}_pF_q({bf a}; {bf b}; z)$ are formulated and proved.
UR - http://www.aot-math.org/article_65772.html
L1 - http://www.aot-math.org/pdf_65772_1103f2a4dda7ee03f7174c00c3490a99.html
ER -