The domain of the Ornstein-Uhlenbeck operator on an -space with invariant measure
We show that the domain of the Ornstein-Uhlenbeck operator on
The eigenvalue problem with conductivity boundary conditions
The eigenvalues of hypoelliptic operators
The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation
The ergodic theory of positive operators on continuous functions
The essential spectrum of holomorphic Toeplitz operators on spaces
We compute the essential Taylor spectrum of a tuple of analytic Toeplitz operators on , where D is a strictly pseudoconvex domain. We also provide specific formulas for the index of provided that is a compact subset of D.
The Existence of Wave Operators in Scattering Theory.
The fine spectra discrete Cesàro operator on .
The Fourier transofrm technique for convolution equations in infinite dimensional lq-spaces.
The Fréchet derivative of an analytic function of a bounded operator with some applications.
The free cover of a row contraction.
The Fuglede-Putnam theorem and Putnam's inequality for quasi-class (A, k) operators.
The Fuglede–Putnam theorem for -quasihyponormal operators.
The geometry of Kato Grassmannians
We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.
The Hadamard product and related dilations
The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
A family T(ν), ν ∈ ℝ, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hull of the canonical basis in ℓ2(ℤ+) are essentially self-adjoint for |ν| ≥ 1 and have deficiency indices (1, 1) for |ν| < 1. A convenient description of all self-adjoint extensions is obtained and the spectral problem is analyzed in detail. The spectrum is discrete and the characteristic equation...
The Hilbert projective metric and an equation in a -algebra
The Hypercyclicity Criterion for sequences of operators
We show that under no hypotheses on the density of the ranges of the mappings involved, an almost-commuting sequence (Tₙ) of operators on an F-space X satisfies the Hypercyclicity Criterion if and only if it has a hereditarily hypercyclic subsequence , and if and only if the sequence (Tₙ ⊕ Tₙ) is hypercyclic on X × X. This strengthens and extends a recent result due to Bès and Peris. We also find a new characterization of the Hypercyclicity Criterion in terms of a condition introduced by Godefroy...
The hypo-Euclidean norm of an -tuple of vectors in inner product spaces and applications.
The index for Fredholm elements in a Banach algebra via a trace
We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.