On the Structure of the Critical Spectrum of Strongly Continuous Semigroups

2019 ◽  
pp. 55-65 ◽  
Author(s):  
Mark Blake ◽  
Simon Brendle ◽  
Rainer Nagel
Keyword(s):  
Strongly Continuous Semigroups ◽  
Critical Spectrum

scholarly journals Conformal Symmetry and Supersymmetry in Rindler Space

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 144
Author(s):  
Jan-Willem van Holten
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Extended Space ◽  
Rindler Space ◽  
Dimensional Space Time ◽  
Critical Spectrum ◽  
Infinite Strings ◽  
Bogoliubov Transformations

This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional space-time. Generically, in addition to a conformal co-ordinate transformation, the transformation of fields from Minkowski to Rindler space is accompanied by local conformal and Lorentz transformations of the components, which also affect the Bogoliubov transformations between the associated Fock spaces. I construct these transformations for massless scalars and spinors, as well as for the ghost and super-ghost fields necessary in theories with local conformal and supersymmetries, as arising from coupling to two-dimensional (2-D) gravity or supergravity. Cancellation of the anomalies in Minkowski and in Rindler space requires theories with the well-known critical spectrum of particles that arise in string theory in the limit of infinite strings, and it is relevant for the equivalence of Minkowski and Rindler frame theories.

scholarly journals Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case

1988 ◽  
Vol 109 (1-2) ◽  
pp. 145-172 ◽  
Author(s):  
Ph. Clément ◽  
O. Diekmann ◽  
M. Gyllenberg ◽  
H. J. A. M. Heijmans ◽  
H. R. Thieme
Keyword(s):  
Banach Space ◽  
Functional Differential Equations ◽  
Time Dependent ◽  
Evolutionary System ◽  
Strongly Continuous Semigroups ◽  
Structured Population ◽  
Variation Of Constants ◽  
Retarded Functional Differential Equations ◽  
Functional Differential ◽  
Age Structured

SynopsisWe consider time-dependent perturbations of generators of strongly continuous semigroups on a Banach space. The perturbations map the Banach space into a bigger space, which is the second dual of the original space in a specific semigroup sense. Using the theory of dual semigroups we show that the solutions of a generalised variation-of-constants formuladefine an evolutionary system. We investigate continuity and differentiability propertiesof this evolutionary system and its dual system and examine in what sense the perturbed generator and its adjoint generate these evolutionary systems. It is shown that the results apply naturally to retarded functional differential equations and age structured population dynamics.

C-semigroups and strongly continuous semigroups

1993 ◽  
Vol 81 (1-2) ◽  
pp. 227-255 ◽  
Author(s):  
Ralph deLaubenfels
Keyword(s):  
Strongly Continuous Semigroups

Uniqueness and critical spectrum of boundary spike solutions

2001 ◽  
Vol 131 (6) ◽  
pp. 1457-1480 ◽  
Author(s):  
Juncheng Wei
Keyword(s):  
Singularly Perturbed Problem ◽  
Curvature Function ◽  
Exact Asymptotics ◽  
Degenerate Critical Point ◽  
Spike Solution ◽  
Critical Spectrum ◽  
The Mean ◽  
Image Position ◽  
Single Boundary ◽  
Small Eigenvalues

We study the properties of single boundary spike solutions for the following singularly perturbed problem It is known that at a non-degenerate critical point of the mean curvature function H(P), there exists a single boundary spike solution. In this paper, we show that the single boundary spike solution is unique and moreover it has exactly (N − 1) small eigenvalues. We obtain the exact asymptotics of the small eigenvalues in terms of H(P).

Wireless communication and spectrum sharing for public safety in the United States

2016 ◽  
Vol 14 (3) ◽  
pp. 167 ◽  
Author(s):  
Naim Kapucu, PhD ◽  
Brittany Haupt, MEd ◽  
Murat Yuksel, PhD
Keyword(s):  
United States ◽  
Wireless Communication ◽  
Communication Systems ◽  
Spectrum Sharing ◽  
Public Safety ◽  
The United States ◽  
Wireless Communication Systems ◽  
Vast Number ◽  
Commercial Market ◽  
Critical Spectrum

With the vast number of fragmented, independent public safety wireless communication systems, the United States is encountering major challenges with enhancing interoperability and effectively managing costs while sharing limited availability of critical spectrum. The traditional hierarchical approach of emergency management does not always allow for needed flexibility and is not a mandate. A national system would reduce equipment needs, increase effectiveness, and enrich quality and coordination of response; however, it is dependent on integrating the commercial market. This article discusses components of an ideal national wireless public safety system consists along with key policies in regulating wireless communication and spectrum sharing for public safety and challenges for implementation.

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