Starting from the D!-Riccati Diierence equation satissed by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the general fourth-order diierence equation satissed by the associated of any integer order of orthogonal polynomials of the-Laguerre-Hahn class. Moreover, in classical situations (Meixner, Charlier, Krawtchouk and Hahn), we give these dii...

We prove a version of Hahn-Banach Theorem. and 1] provide the notation and terminology for this paper. The following propositions are true: (1) For all sets x, y and for every function f such that h hx; yi i 2 f holds y 2 rng f: (2) For every set X and for all functions f, g such that X dom f and f g holds fX = gX: (3) For every non empty set A and for every set b such that A 6 = fbg there exis...

We describe an implementation of a pointfree proof of the Alaoglu and the Hahn-Banach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in \The Hahn-Banach Theorem in Type Theory" 4]. The implementation was partially developed simultaneously with 4] and it was a help in the development of the informal proofs.

We consider real spaces only. Definition. An operator T : X → Y between Banach spaces X and Y is called a Hahn-Banach operator if for every isometric embedding of the space X into a Banach space Z there exists a norm-preserving extension T̃ of T to Z. A geometric property of Hahn-Banach operators of finite rank acting between finite-dimensional normed spaces is found. This property is used to ch...

Abstract About two dozens of exactly solvable Markov chains on one-dimensional finite and semi-infinite integer lattices are constructed in terms convolutions orthogonality measures the Krawtchouk, Hahn, Meixner, Charlier, q-Hahn, q-Meixner little q-Jacobi polynomials. By construction, stationary probability distributions, complete sets eigenvalues eigenvectors provided by polynomials measures. A...