Abstract This short note is concerned with various operator representations of frames in a Hilbert space $${{{\mathcal {H}}}}.$$ H . While it known that only very special can be represented the form $$\{ T^n \varphi \}_{n=0}^\infty $$ { <m...

Abstract It is shown that the extensions of exactly-solvable quantum mechanical problems connected with replacement ordinary derivatives by Dunkl ones and classical orthogonal polynomials exceptional can be easily combined. For such a purpose, example oscillator on line considered three different types rationally-extended oscillators are constructed. The corresponding wavefunctions expressed in...

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).