scholarly journals Lecture notes : Spectral properties of non-self-adjoint operators

2009 ◽  
pp. 1-111 ◽  
Author(s):  
Johannes Sjöstrand
Keyword(s):  
Spectral Properties ◽  
Lecture Notes ◽  
Adjoint Operators

scholarly journals INTEGER OPERATORS IN FINITE VON NEUMANN ALGEBRAS

2011 ◽  
Vol 03 (04) ◽  
pp. 433-450
Author(s):  
ANDREAS THOM
Keyword(s):  
Potential Theory ◽  
Spectral Properties ◽  
Von Neumann Algebras ◽  
Logarithmic Capacity ◽  
Integral Group ◽  
Von Neumann ◽  
Classical Potential ◽  
Classical Potential Theory ◽  
Adjoint Operators ◽  
Finite Von Neumann Algebras

Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle of results obtained by Fekete and Szegö, see [3, 4, 13]. More concretely, we use results by Rumely, see [12], on equidistribution of algebraic integers to obtain a description of those integer operator which have spectrum of logarithmic capacity less than or equal to one. Finally, we relate the study of integer operators to a recent construction by Petracovici and Zaharescu, see [10].

scholarly journals On local spectral properties of Hamilton operators

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2563-2566
Author(s):  
Wurichaihu Bai ◽  
Alatancang Chen
Keyword(s):  
Spectral Properties ◽  
Hyperinvariant Subspace ◽  
Weyl Type Theorems ◽  
Subspace Problem ◽  
Adjoint Operators

This paper deals with local spectral properties of Hamilton type operators. The strongly decomposability, Weyl type theorems and hyperinvariant subspace problem of them and the similar properties with their adjoint operators are studied. As corollaries, some local spectral properties of Hamilton operators are obtained.

scholarly journals Spectral Enclosures and Complex Resonances for General Self-Adjoint Operators

1998 ◽  
Vol 1 ◽  
pp. 42-74 ◽  
Author(s):  
E.B. Davies
Keyword(s):  
Spectral Properties ◽  
Linear Subspace ◽  
Adjoint Operator ◽  
Dimensional Linear Subspace ◽  
Finite Dimensional ◽  
Adjoint Operators ◽  
Computation Of Eigenvalues

AbstractThis paper considers a number of related problems concerning the computation of eigenvalues and complex resonances of a general self-adjoint operator H. The feature which ties the different sections together is that one restricts oneself to spectral properties of H which can be proved by using only vectors from a pre-assigned (possibly finite-dimensional) linear subspace L.

scholarly journals Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Arezoo Ghaedrahmati ◽  
Ali Sameripour
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Spectral Properties ◽  
Differential Operators ◽  
Dimensional Space ◽  
The Other ◽  
Heat Equations ◽  
Elliptic Differential Operator ◽  
Other Hand ◽  
Adjoint Operators

Non-self-adjoint operators have many applications, including quantum and heat equations. On the other hand, the study of these types of operators is more difficult than that of self-adjoint operators. In this paper, our aim is to study the resolvent and the spectral properties of a class of non-self-adjoint differential operators. So we consider a special non-self-adjoint elliptic differential operator (Au)(x) acting on Hilbert space and first investigate the spectral properties of space H 1 = L 2 Ω 1 . Then, as the application of this new result, the resolvent of the considered operator in ℓ -dimensional space Hilbert H ℓ = L 2 Ω ℓ is obtained utilizing some analytic techniques and diagonalizable way.

Spectral properties of two parameter eigenvalue problems II

1987 ◽  
Vol 106 (1-2) ◽  
pp. 39-51 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Eigenvalue Problems ◽  
Separable Hilbert Space ◽  
Asymptotic Properties ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Adjoint Operators ◽  
Bounded Below ◽  
Two Parameter

SynopsisWe consider eigenvalues λ =(λ1, λ2) ∈R2 for the problem W(λ)x = 0, x ≠ 0, x ∈ H, where W(λ) = R + λ1V1 + λ2V2), and R, V1, V2 are self-adjoint operators on a separable Hilbert space H, R being bounded below with compact resolvent and V1, V2 being bounded. The i-th eigencurve Z1 is the set of eigenvalues λ, for which the i-th eigenvalue (counted according to multiplicity and in increasing order) of W(λ) vanishes. We study monotonic and asymptotic properties of Zi, and we give formulae for any asymptotes that exist. Additional results are given in the finite dimensional case.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

Structure and Spectral Properties of New Composites Based on Metal Alkanoates with Gold Nanoparticles

2015 ◽  
Vol 60 (04) ◽  
pp. 356-361 ◽  
Author(s):  
A. Tolochko ◽  
◽  
P. Teselko ◽  
A. Lyashchova ◽  
D. Fedorenko ◽  
...  
Keyword(s):  
Gold Nanoparticles ◽  
Spectral Properties
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