A Short Proof of the Ando-Krieger Theorem.
A short proof of the best possibility for the grand Furuta inequality.
A Simple Example of Localized Parametric Resonance for the Wave Equation
2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.The problem studied here was suggested to us by V. Petkov. Since the beginning of our careers, we have benefitted from his insights in partial differential equations and mathematical physics. In his writings and many discussions, the conjuction of deep analysis and specially interesting problems has been a source inspiration for us.The research of J. Rauch is partially supported by the U.S. National Science Foundation under grant NSF-DMS-0104096...
A singular functional-differential equation.
A smooth subadditive homogeneous norm on a homogeneous group
A space by W. Gowers and new results on norm and numerical radius attaining operators
A Spectral Gap Theorem for Dirac Operators with Central Field.
A spectral mapping theorem for Banach modules
Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then for each measure μ in reg(M(G)), where denotes the operator in B(X) defined by , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all...
A spectral mapping theorem for functions with finite Dirichlet integral.
A Spectral Mapping Theorem for Holomorphic Functions.
A Spectral Mapping Theorem for Local Multipliers.
A spectral mapping theorem for perturbed strongly continuous semigroups.
A spectral mapping theorem for semigroups solving PDEs with nonautonomous past.
A spectral perturbation problem and its applications to waves above an underwater ridge.
A spectral study of an infinite axisymmetric elastic layer
We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators , , in a suitable Hilbert space. We show that the essential spectrum of is an interval of type and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.
A spectral study of an infinite axisymmetric elastic layer
We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, , in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.
A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras
Let A be a commutative Banach algebra with Gelfand space ∆ (A). Denote by Aut (A) the group of all continuous automorphisms of A. Consider a σ(A,∆(A))-continuous group representation α:G → Aut(A) of a locally compact abelian group G by automorphisms of A. For each a ∈ A and φ ∈ ∆(A), the function t ∈ G is in the space C(G) of all continuous and bounded functions on G. The weak-star spectrum is defined as a closed subset of the dual group Ĝ of G. For φ ∈ ∆(A) we define to be the union of all...
A structure theory for isometric representations of a class of semigroups.
A study of resolvent set for a class of band operators with matrix elements
For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.
A survey of certain trace inequalities
This paper concerns inequalities like TrA ≤ TrB, where A and B are certain Hermitian complex matrices and Tr stands for the trace. In most cases A and B will be exponential or logarithmic expressions of some other matrices. Due to the interest of the author in quantum statistical mechanics, the possible applications of the trace inequalities will be commented from time to time. Several inequalities treated below have been established in the context of Hilbert space operators or operator algebras....