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Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński (2009)

Studia Mathematica

We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning perturbations...

Solvability conditions for some difference operators.

Apreutesei, N.C., Volpert, V.A. (2005)

Advances in Difference Equations [electronic only]

Some counterexamples to subexponential growth of orthogonal polynomials

Marcin Zygmunt (1995)

Studia Mathematica

We give examples of polynomials p(n) orthonormal with respect to a measure μ on ⨍ such that the sequence {p(n,x)} has exponential lower bound for some points x of supp μ. Moreover, the set of such points is dense in the support of μ.

Special solutions of linear difference equations with infinite delay

Milan Medveď (1994)

Archivum Mathematicum

For the difference equation $(ϵ) x_{n + 1} = A x_{n} + ϵ \sum_{k = - \infty}^{n} R_{n - k} x_{k}$ ,where $x_{n} \in Y, Y$ is a Banach space, $ϵ$ is a parameter and $A$ is a linear, bounded operator. A sufficient condition for the existence of a unique special solution $y = {y_{n}}_{n = - \infty}^{\infty}$ passing through the point $x_{0} \in Y$ is proved. This special solution converges to the solution of the equation (0) as $ϵ \to 0$ .

Spectral analysis of a weighted shift operator with unbounded operator coefficients.

Baskakov, A.G., Pastukhov, A.I. (2001)

Sibirskij Matematicheskij Zhurnal

Spectral deformations of Jacobi operators.

Gerald Teschl (1997)

Journal für die reine und angewandte Mathematik

Spectral theory from the second-order $q$ -difference operator.

Dhaouadi, Lazhar (2007)

International Journal of Mathematics and Mathematical Sciences

Spectral transition parameters for a class of Jacobi matrices

Joanne Dombrowski, Steen Pedersen (2002)

Studia Mathematica

This paper initially considers a class of unbounded Jacobi matrices defined by an increasing sequence of repeated weights. Spectral parameters are then introduced in various ways to allow the authors to study the nature and location of the spectrum as a function of these parameters.

Spektraltheorie linksdefiniter Differenzengleichungssysteme.

Heinz-Dieter Niessen (1975)

Journal für die reine und angewandte Mathematik

Stability and Convergence Rates in Lp for Certain Difference Schemes.

Philip Brenner, Vidar Thomée (1970)

Mathematica Scandinavica

Sulle equazioni alle differenze con incrementi variabili.

Constanza Borelli Forti, István Fenyö (1980)

Stochastica

Let X be an arbitrary Abelian group and E a Banach space. We consider the difference-operators ∆n defined by induction:(∆f)(x;y) = f(x+y) - f(x), (∆nf)(x;y1,...,yn) = (∆n-1(∆f)(.;y1)) (x;y2,...,yn)(n = 2,3,4,..., ∆1=∆, x,yi belonging to X, i = 1,2,...,n; f: X --> E).Considering the difference equation (∆nf)(x;y1,y2,...,yn) = d(x;y1,y2,...,yn) with independent variable increments, the most general solution is given explicitly if d: X x Xn --> E is a given bounded function. Also the...

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