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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.

Spectral Theory of Singular Hahn Difference Equation of the Sturm-Liouville Type

Bilender P. Allahverdiev, Hüseyin Tuna (2020)

Communications in Mathematics

In this work, we consider the singular Hahn difference equation of the Sturm-Liouville type. We prove the existence of the spectral function for this equation. We establish Parseval equality and an expansion formula for this equation on a semi-unbounded interval.

Stability in linear neutral difference equations with variable delays

Abdelouaheb Ardjouni, Ahcene Djoudi (2013)

Mathematica Bohemica

In this paper we use the fixed point method to prove asymptotic stability results of the zero solution of a generalized linear neutral difference equation with variable delays. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Y. N. Raffoul (2006), E. Yankson (2009), M. Islam and E. Yankson (2005).

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