We use the "tridiagonal representation approach" to solve time-independent Schr\"odinger equation for bound states of generalized versions trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials do not belong conventional class exactly problems. The solutions are finite series square integrable functions written in terms Jacobi polynomial.

For a square integrable vector-valued process f on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for f are presented. The process f is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for f involving the biorthogo...

Abstract. In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study the Fourier and Fourier-Plancherel transforms and prove the Plancherel theorem for compact groupoids. We also study the central functions in the algebra of squa...