98 research outputs found
Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions
In this work, we study the stable determination of four space-dependent
coefficients appearing in a coupled semilinear parabolic system with variable
diffusion matrices subject to dynamic boundary conditions which couple
intern-boundary phenomena. We prove a Lipschitz stability result for interior
and boundary potentials by means of only one observation component, localized
in any arbitrary open subset of the physical domain. The proof mainly relies on
some new Carleman estimates for dynamic boundary conditions of surface
diffusion type
Boundary relations and generalized resolvents of symmetric operators
The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint
exit space extensions of a, not necessarily densely defined, symmetric
operator, in terms of maximal dissipative (in \dC_+) holomorphic linear
relations on the parameter space (the so-called Nevanlinna families). The new
notion of a boundary relation makes it possible to interpret these parameter
families as Weyl families of boundary relations and to establish a simple
coupling method to construct the generalized resolvents from the given
parameter family. The general version of the coupling method is introduced and
the role of boundary relations and their Weyl families for the
Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page
De Branges spaces and Krein's theory of entire operators
This work presents a contemporary treatment of Krein's entire operators with
deficiency indices and de Branges' Hilbert spaces of entire functions.
Each of these theories played a central role in the research of both renown
mathematicians. Remarkably, entire operators and de Branges spaces are
intimately connected and the interplay between them has had an impact in both
spectral theory and the theory of functions. This work exhibits the
interrelation between Krein's and de Branges' theories by means of a functional
model and discusses recent developments, giving illustrations of the main
objects and applications to the spectral theory of difference and differential
operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors
were corrected. The bibliography style was change
The class of n-entire operators
We introduce a classification of simple, regular, closed symmetric operators
with deficiency indices (1,1) according to a geometric criterion that extends
the classical notions of entire operators and entire operators in the
generalized sense due to M. G. Krein. We show that these classes of operators
have several distinctive properties, some of them related to the spectra of
their canonical selfadjoint extensions. In particular, we provide necessary and
sufficient conditions on the spectra of two canonical selfadjoint extensions of
an operator for it to belong to one of our classes. Our discussion is based on
some recent results in the theory of de Branges spaces.Comment: 33 pages. Typos corrected. Changes in the wording of Section 2.
References added. Examples added. arXiv admin note: text overlap with
arXiv:1104.476
Prospective study to assess tumour necrosis factor alpha in non-inflammatory bowel disease enterocutaneous fistula
Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions
© 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.fi=vertaisarvioitu|en=peerReviewed
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