  This paper addresses a new characterization of Sudarshan's diagonal
representation of the density matrix elements $\rho(z',z)$, derivedfrom
$(q;l,\lambda)-$deformed boson coherent states.The induced $\rho(z',z)$
self-reproducing property with the associated self-reproducing kernel $K(z',z)$
is computed and analyzed. An explicit construction of novel classes of
generalized continuous $(q;l,\lambda)-$Hermite polynomials is provided with the
corresponding recursion relations and exact resolution of the moment problems
giving their orthogonality weight functions. Besides, the
Berezin-Klauder-Toeplitz quantization of classical phase space observables and
relevant normal and anti-normal forms are investigated and discussed.
