Eigenfunction expansions for nondensely defined differential operators

Eigenfunction Expansions for Nondensely De- Fined Operators Generated by Symmetric Ordinary Differential Expressions by Earl A. Coddington

where the pk are complex-valued functions of class C k on an interval a < x < b, and pn(x) / 0 there. In the Hilbert space § = 2 {a, b) let S0 be the closure in § 2 of the set of all {ƒ, Lf} for ƒ e C$(a, b), the functions in C°°(a,b) vanishing outside compact subintervals of a < x < b. This S0 in a closed densely defined symmetric operator whose adjoint has the domain 3>(S$), the set of all ƒ ...

Complex Powers of Nondensely Defined Operators

The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...

Existence Results for Semilinear Perturbed Functional Differential Equations with Nondensely Defined Operators

Eigenfunction Expansions for Schrödinger Operators on Metric Graphs

We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

Eigenfunction Expansions for Some Nonselfadjoint Operators and the Transport Equation*

There are many papers dealing with various aspects of the perturbation theory of a continuous spectrum [l-5, 12-151. In [3-51 some problems with nonselfadjoint operators were considered. In [3b] conditions for the perturbed operator to be similar to the unperturbed one are given. In [4] the Schrijdinger operator with a complex-valued potential was considered. In [S ] a theorem is announced in w...