Discrete spectra criteria for singular difference operators

Simón Peňa

Displaying similar documents to “Discrete spectra criteria for singular difference operators”

Higher-order differential systems and a regularization operator

Pavel Calábek (1999)

Mathematica Bohemica

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Sufficient conditions for the existence of solutions to boundary value problems with a Caratheodory right hand side for ordinary differential systems are established by means of continuous approximations.

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $ℓ (y) \equiv \frac{1}{w (t)} (r (t) y)$ , $t \in [a, \infty)$ are established. These conditions are based on a recently proved relationship between spectral properties of $ℓ$ and oscillation of a certain associated second order differential equation.

Linear Stieltjes integral equations in Banach spaces

Štefan Schwabik (1999)

Mathematica Bohemica

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Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in []. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. []). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the...

A second look on definition and equivalent norms of Sobolev spaces

Joachim Naumann, Christian G. Simader (1999)

Mathematica Bohemica

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Sobolev’s original definition of his spaces $L^{m, p} (Ω)$ is revisited. It only assumed that $Ω \subseteq ℝ^{n}$ is a domain. With elementary methods, essentially based on Poincare’s inequality for balls (or cubes), the existence of intermediate derivates of functions $u \in L^{m, p} (Ω)$ with respect to appropriate norms, and equivalence of these norms is proved.