On the boundary spectrum of dominatedC o-Semigroups

1989 ◽  
Vol 38 (1) ◽  
pp. 129-139 ◽  
Author(s):  
F. Andreu ◽  
J. M. Maźon
Keyword(s):  
Boundary Spectrum

Regularity-type properties of the boundary spectrum in Banach algebras

2019 ◽  
Vol 49 (8) ◽  
pp. 2747-2754
Author(s):  
Heinrich Raubenheimer ◽  
Andre Swartz
Keyword(s):  
Banach Algebras ◽  
Boundary Spectrum

scholarly journals Operator expansions, layer susceptibility and two-point functions in BCFT

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Parijat Dey ◽  
Tobias Hansen ◽  
Mykola Shpot
Keyword(s):  
Correlation Function ◽  
Power Series Expansion ◽  
Operator Product ◽  
Point Function ◽  
Direct Identification ◽  
Boundary Spectrum ◽  
Anomalous Dimensions ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Expansion Coefficients

Abstract We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function 〈ϕiϕi〉 of the O(N) model at the extraordinary transition in 4 − ϵ dimensional semi-infinite space to order O(ϵ). The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order O(ϵ2). These agree with the known results both in ϵ and large-N expansions.

scholarly journals On the existence of high-frequency boundary resonances in layered elastic media

2015 ◽  
Vol 471 (2178) ◽  
pp. 20140878 ◽  
Author(s):  
K. D. Cherednichenko ◽  
S. Cooper
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
High Frequency ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Elastic Media ◽  
Displacement Boundary ◽  
Boundary Spectrum ◽  
New Type ◽  
High Frequency Vibrations

We analyse the asymptotic behaviour of high-frequency vibrations of a three-dimensional layered elastic medium occupying the domain Ω =(− a , a ) 3 , a >0. We show that in both cases of stress-free and zero-displacement boundary conditions on the boundary of Ω a version of the boundary spectrum, introduced in Allaire and Conca (1998 J. Math. Pures. Appl. 77, 153–208. ( doi:10.1016/S0021-7824(98)80068-8 )), is non-empty and part of it is located below the Bloch spectrum. For zero-displacement boundary conditions, this yields a new type of surface wave, which is absent in the case of a homogeneous medium.

Boundary spectrum of nonnegative operators

1986 ◽  
Vol 26 (6) ◽  
pp. 798-802
Author(s):  
A. I. Veitsblit ◽  
Yu. I. Lyubich
Keyword(s):  
Boundary Spectrum
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