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A family T(ν), ν ∈ ℝ, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hull of the canonical basis in ℓ2(ℤ+) are essentially self-adjoint for |ν| ≥ 1 and have deficiency indices (1, 1) for |ν| < 1. A convenient description of all self-adjoint extensions is obtained and the spectral problem is analyzed in detail. The spectrum is discrete and the characteristic equation...

The Helmholtz conditions for the difference equations systems.

Crăciun, Dumitru, Opriş, Dumitru (1996)

Balkan Journal of Geometry and its Applications (BJGA)

The Hyers-Ulam stability for two functional equations in a single variable.

Miheţ, Dorel (2008)

Banach Journal of Mathematical Analysis [electronic only]

The Hyers-Ulam-Aoki Type Stability of Some Functional Equations on Banach Lattices

Nutefe Kwami Agbeko (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.

The $l^{p}$ trichotomy for difference systems and applications

Serena Matucci (2000)

Archivum Mathematicum

The laplacian and the discrete laplacian

Z. Ditzian (1989)

Compositio Mathematica

The lattice structure of connection preserving deformations for $q$ -Painlevé equations I.

Ormerod, Christopher M. (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The law of large numbers and a functional equation

Maciej Sablik (1998)

Annales Polonici Mathematici

We deal with the linear functional equation (E) $g (x) = \sum_{i = 1}^{r} p_{i} g (c_{i} x)$ , where g:(0,∞) → (0,∞) is unknown, $(p ₁, . . ., p_{r})$ is a probability distribution, and $c_{i}$ ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.

The Levi-Civita equation, vector modules and spectral synthesis

László Székelyhidi (2013)

Banach Center Publications

The purpose of this paper is to give a survey on some recent results concerning spectral analysis and spectral synthesis in the framework of vector modules and in close connection with the Levi-Civita functional equation. Further, we present some open problems in this subject.

The local structure of the solutions of the multidimensional translation equation.

Lothar Berg (1993)

Aequationes mathematicae

The matrix equation a(x...y) = a(x) + a(x)a(y) + a(y).

M.A. McKiernan (1977)

Aequationes mathematicae

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