Displaying similar documents to “A characterization of multiplication by the independent variable on ℒ p ”

Operators preserving orthogonality of polynomials

Francisco Marcellán, Franciszek Szafraniec (1996)

Studia Mathematica

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Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions...

Reflexivity of isometries

Wing-Suet Li, John McCarthy (1997)

Studia Mathematica

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We prove that any set of commuting isometries on a separable Hilbert space is reflexive.

On certain generalized q-Appell polynomial expansions

Thomas Ernst (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...

Linearization of Arbitrary products of classical orthogonal polynomials

Mahouton Hounkonnou, Said Belmehdi, André Ronveaux (2000)

Applicationes Mathematicae

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A procedure is proposed in order to expand w = ∏ j = 1 N P i j ( x ) = ∑ k = 0 M L k P k ( x ) where P i ( x ) belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) ( M = ∑ j = 1 N i j ). We first derive a linear differential equation of order 2 N satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients L k . We develop in detail the two cases [ P i ( x ) ] N , P i ( x ) P j ( x ) P k ( x ) and give the recurrencerelation in some cases (N=3,4), when the polynomials P i ( x ) are monic Hermite orthogonal polynomials.