The singular sequence problem
The Singularity Expansion Method applied to the transient motions of a floating elastic plate
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
The Słodkowski spectra and higher Shilov boundaries
We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)
Kato’s conjecture, stating that the domain of the square root of any accretive operator with bounded measurable coefficients in is the Sobolev space , i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.
The spectra and singular values of multidimensional integral operators with bihomogeneous kernels.
The spectra of general differential operators in the direct sum spaces
In this paper, the general ordinary quasi-differential expression of -th order with complex coefficients and its formal adjoint on any finite number of intervals , , are considered in the setting of the direct sums of -spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations...
The spectral mapping theorem for integrated semigroups.
The spectral mapping theorem for one-parameter groups of positive operators on C0(X).
The spectral mapping theorem for the essential approximate point spectrum
The spectral radii of an operator and its modulus
The spectrally bounded linear maps on operator algebras
We show that every spectrally bounded linear map Φ from a Banach algebra onto a standard operator algebra acting on a complex Banach space is square-zero preserving. This result is used to show that if Φ₂ is spectrally bounded, then Φ is a homomorphism multiplied by a nonzero complex number. As another application to the Hilbert space case, a classification theorem is obtained which states that every spectrally bounded linear bijection Φ from ℬ(H) onto ℬ(K), where H and K are infinite-dimensional...
The spectrum and commutant of a certain weighted translation operator.
The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential.
The spectrum of a class of almost periodic operators.
The Spectrum Of Infinite Complite Multipartite Graphs
The Spectrum of the Continuous Laplacian on a Graph.
The splitting spectrum differs from the Taylor spectrum
We construct a pair of commuting Banach space operators for which the splitting spectrum is different from the Taylor spectrum.
The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...
The stability of tachyonic field system by factorization method.
The Stability of the Euler Characteristic for Hilbert Complexes.