English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We continue the study of boundary data maps, that is, generalizations ofspectral parameter dependent Dirichlet-to-Neumann maps for (three-coefficient)Sturm-Liouville operators on the finite interval $(a,b)$, to more generalboundary conditions. While earlier studies of boundary data maps focused on thecase of general separated boundary conditions at $a$ and $b$, the present workdevelops a unified treatment for all possible self-adjoint boundary conditions(i.e., separated as well as non-separated ones).  In the course of this paper we describe the connections with Krein'sresolvent formula for self-adjoint extensions of the underlying minimalSturm-Liouville operator (parametrized in terms of boundary conditions), withsome emphasis on the Krein extension, develop the basic trace formulas forresolvent differences of self-adjoint extensions, especially, in terms of theassociated spectral shift functions, and describe the connections betweenvarious parametrizations of all self-adjoint extensions, including the preciserelation to von Neumann's basic parametrization in terms of unitary mapsbetween deficiency subspaces.

Boundary Data Maps and Krein's Resolvent Formula for Sturm-Liouville Operators on a Finite Interval