Search results for "Matrix"
showing 10 items of 3205 documents
Fredholm Spectra and Weyl Type Theorems for Drazin Invertible Operators
2016
In this paper we investigate the relationship between some spectra originating from Fredholm theory of a Drazin invertible operator and its Drazin inverse, if this does exist. Moreover, we study the transmission of Weyl type theorems from a Drazin invertible operator R, to its Drazin inverse S.
Local Spectral Properties Under Conjugations
2021
AbstractIn this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and $$T\in L(H)$$ T ∈ L ( H ) . We also study the relationship between the quasi-nilpotent part of the adjoint $$T^*$$ T ∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form $$JT^*J$$ J T ∗ J . The theory is exemplified in some concrete cases.
On the Rational Homogeneous Manifold Structure of the Similarity Orbits of Jordan Elements in Operator Algebras
1991
Considering a topological algebra B with unit e, an open group of invertible elements B −1 and continuous inversion (e. g. B = Banach algebra, B = C∞(Ω, M n (ℂ)) (Ω smooth manifold), B = special algebras of pseudo-differential operators), we are going to define the set of Jordan elements J ⊂ B (such that J = Set of Jordan operators if B = L(H), H Hilbert space) and to construct rational local cross sections for the operation mapping $$ {B^{ - 1}} \mathrel\backepsilon g \mapsto gJ{g^{ - 1}} $$ of B −1 on the similarity orbit S(J):= {gJg −1: g Є B −1}, J Є J.
Evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in metric random walk spaces
2019
Abstract In this paper we study evolution problems of Leray–Lions type with nonhomogeneous Neumann boundary conditions in the framework of metric random walk spaces. This covers cases with the p -Laplacian operator in weighted discrete graphs and nonlocal operators with nonsingular kernel in R N .
Decomposition numbers and local properties
2020
Abstract If G is a finite group and p is a prime, we give evidence that the p-decomposition matrix encodes properties of p-Sylow normalizers.
Multiple Points in the Target: The Case of Parameterised Hypersurfaces
2020
We focus on parameterised hypersurfaces, and explore the information one can obtain from the matrix of a presentation of the push-forward of the structure sheaf, through the use of Fitting ideals. We show that in a number of cases the spaces defined by the Fitting ideals are Cohen–Macaulay, extending the previously known range. We prove the Milnor–Tjurina relation for parameterised hypersurfaces whose dimension is no greater than two.
A note on k-generalized projections
2007
Abstract In this note, we investigate characterizations for k -generalized projections (i.e., A k = A ∗ ) on Hilbert spaces. The obtained results generalize those for generalized projections on Hilbert spaces in [Hong-Ke Du, Yuan Li, The spectral characterization of generalized projections, Linear Algebra Appl. 400 (2005) 313–318] and those for matrices in [J. Benitez, N. Thome, Characterizations and linear combinations of k -generalized projectors, Linear Algebra Appl. 410 (2005) 150–159].
OMA: From Research to Engineering Applications
2021
Ambient vibration modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., when there is no initial excitation or known artificial excitation. This method for testing and/or monitoring historical buildings and civil structures, is particularly attractive for civil engineers concerned with the safety of complex historical structures. However, in practice, not only records of external force are missing, but uncertainties are involved to a significant extent. Hence, stochastic mechanics approaches are needed in combination with the iden…
Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization
1999
In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut A(t)uxx B(t)u=0; 0 0, u(0;t)=u(p;t)=0; u(x;0)=f(x);06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given >0 and t0;t1; with 0<t0<t1 and D(t0;t1)=f(x;t); 06x6p; t06t6t1g the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0;t1). An algorithm is also included. c 1999 Elsevier Science B.V. All rights reserved. AMS classication: 65M15, 34A50, 35C10, 35A50
Differential identities, 2 × 2 upper triangular matrices and varieties of almost polynomial growth
2019
Abstract We study the differential identities of the algebra U T 2 of 2 × 2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L = Der ( U T 2 ) of derivations of U T 2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group S n and we determine the decomposition of the corresponding character into irreducibles. If V is the variety of differential algebras generated by U T 2 , we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almo…