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Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

Equation[1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y))has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]:[2] f(x+1) + f (f(x)+1) = 1,[3] f(2x) + f(2f(x)) = f(2f(x + f(x))).Equation [3] leads to a Cauchy functional equation:[4] phi(f(x)+x) = phi(f(x)) + phi(x),restricted to the graph of the function f,...

Some remarks on the stability of the multi-Jensen equation

Jens Schwaiger (2013)

Open Mathematics

First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in...

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 ∑ k = - ∞ n R n - k x k ,where x n ∈ 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 = - ∞ ∞   passing through the point  x 0 ∈ Y   is proved. This special solution converges to the solution of the equation (0) as  ϵ → 0 .

Spectral analysis of unbounded Jacobi operators with oscillating entries

Jan Janas, Marcin Moszyński (2012)

Studia Mathematica

We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...

Spectral theory of corrugated surfaces

Vojkan Jakšić (2001)

Journées équations aux dérivées partielles

We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.

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