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Spectral Analysis on Graph-like Spaces (Lecture Notes in Mathematics, Vol. 2039) - Softcover

Post, Olaf

 
9783642238390: Spectral Analysis on Graph-like Spaces (Lecture Notes in Mathematics, Vol. 2039)
Softcover
ISBN 10: 3642238394 ISBN 13: 9783642238390
Publisher: Springer, 2012

Synopsis

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.

"synopsis" may belong to another edition of this title.

From the Back Cover

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis.

In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances.

Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as

-norm convergence of operators acting in different Hilbert
spaces,

- an extension of the concept of boundary triples to partial
differential operators, and

-an abstract definition of resonances via boundary triples.

These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2012
Language
English
ISBN 10 
3642238394
ISBN 13 
9783642238390
Binding
Paperback
Edition number
1
Number of pages
446