Approximate antilinear eigenvalue problems and related inequalities

Approximate Antilinear Eigenvalue Problems and Related Inequalities

If T is a complex symmetric operator on a separable complex Hilbert space H, then the spectrum σ(|T |) of √ T ∗T can be characterized in terms of a certain approximate antilinear eigenvalue problem. This approach leads to a general inequality (applicable to any bounded operator T : H → H), in terms of the spectra of the selfadjoint operators ReT and ImT , restricting the possible location of el...

Eigenvalue Problems Associated with Korn's Inequalities

Quantum inequalities and ‘quantum interest’ as eigenvalue problems

Quantum inequalities (QI’s) provide lower bounds on the averaged energy density of a quantum field. We show how the QI’s for massless scalar fields in even dimensional Minkowski space may be reformulated in terms of the positivity of a certain self-adjoint operator—a generalized Schrödinger operator with the energy density as the potential—and hence as an eigenvalue problem. We use this idea to...

The application of isoperimetric inequalities for nonlinear eigenvalue problems

Our aim is to show the interplay between geometry analysis and applications of the theory of isoperimetric inequalities for some nonlinear problems. Reviewing the isoperimetric inequalities valid on Minkowskian plane we show that we can get estimations of physical quantities, namely, estimation on the first eigenvalue of nonlinear eigenvalue problems, on the basis of easily accessible geometric...

Perturbation Results Related to Palindromic Eigenvalue Problems

We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ)= λ2 A?1 + λA0 + A1 with A0, A1 ∈ C n×n and A?0 = A0 (where ?= T or H ). The perturbation of eigenvalues in the context of general matrix polynomials, palindromic pencils, (semi-Schur) anti-triangular canonical forms and differentiation is discussed. 2000 Mathematics subject classification: primar...