Showing papers in "Journal of Functional Analysis in 1976"

TL;DR: In this article, the authors extend the Prekopa-leindler theorem to other types of convex combinations of two positive functions and strengthen it by introducing the notion of essential addition.

TL;DR: In this paper, a-projections (projection par rapport a forme bilineaire a nonnecessairement symetrique) sont etudiees dans les Chapitres 2 and 3.

TL;DR: In this article, the authors studied the discrete part of the regular representation of a locally compact group and also its Type I part if the group is separable and established orthogonality relations for matrix coefficients of square integrable representations and showed that the formal degree in general is not a positive number, but a positive self-adjoint unbounded operator, semi-invariant under the representation.

TL;DR: In this article, it was shown that the solution of the Stokes problem has square integrable second derivatives provided that the domain is a convex polygon in the plane and the nonhomogeneous term is square integral.

TL;DR: In this paper, it was shown that W∗-algebras, with the exception of certain finite type I's, are not nuclear, and that these norms, with α and ν, can be mutually distinct.

TL;DR: In this article, the authors studied the approximation properties of complex valued holomorphic functions on a complex Banach space and showed that the compact-open topology has the approximation property if and only if E has the approximate property.

TL;DR: In this article, it was shown that the scattering for − Δ + V is complete if and only if that for W = Vχ where W is the characteristic function of the exterior of a ball.

TL;DR: In this article, it was shown that in a C∗-algebra every derivation of which is determined by a multiplier is equivalent to the restriction of the automorphism to some invariant essential closed two-sided ideal.

TL;DR: The primitive ideal space of the group C ∗ -algebra of a discrete finitely generated solvable group is T 1 if and only if the group is a finite extension of a nilpotent group as discussed by the authors.

TL;DR: In this article, it was shown that a global conclusion for the implicit function theorem with no additonal hypotheses is possible with no additional assumptions on the underlying structure of the graph.

TL;DR: In this article, the authors show that the linear forms associated to "infinitely good elements" of V, separate points in V, carry then a well-defined self-dual structure.

TL;DR: In this paper, a general theory of operator-valued Bessel functions is presented, which arise naturally in representation theory in the context of metaplectic representations, discrete series, and limits of discrete series for certain semi-simple Lie groups.

TL;DR: In this paper, the spectrum and multiplicities of irreducible unitary representations appearing in the quasi-regular representation U were calculated using the Poisson summation formula.

TL;DR: In this article, it was shown that the ring H ∞ of bounded analytic functions in the unit disc is coherent, while the disc algebra A is not coherent, for any positive measure μ, L∞(μ) is coherent.

TL;DR: In this article, the abstract stationary theory of Kato and Kuroda is applied to multichannel scattering problems and it is shown that stationary wave operators exist and are asymptotically complete whenever the resolvent can be completely described in terms of primary singularities for a commuting family of channel Hamiltonians.

TL;DR: In this article, the Radon-Nikodym property of a closed bounded convex subset of a Banach space has been studied in the context of convex sets with Borel probability measures.

TL;DR: In this article, a class of integral operators on L p spaces is studied, where the operator I − K is invertible on L r and L s but not on l p for some p between r and s.

TL;DR: In this paper, the authors define le plus petit prolongement ferme de l'operateur de domaine D(V) as: x ϵ D (V) → ax + ∝ V(I + λV)−1 x dμ(λ) (avec a ⩾ 0 and μ mesure positive sur R + verifiant ∝ (dμ(t) (1 + t)) dμ

TL;DR: In this article, Mitiagin and Zobin constructed an example of nuclear Frechet space without basis, and the essential modification of their constructions gives the following results: (1) there exists such a nuclear Freche space X that for any nuclear frechet space Y the space X × Y has no basis (Sections 1 and 2).

TL;DR: In this article, the authors studied linear operators between non-degenerate partial inner product spaces and their relationships to self-adjoint operators in a "middle" Hilbert space, and showed that linear operators can be expressed as

TL;DR: In this article, the authors introduce the classes of mixed smoothness L α p (R n ), L α P (Z n ) for a multi-index α = ( α 1,…, α n ).

TL;DR: In this paper, it was shown that the intersection of all nonzero closed invariant ideals is zero, even when the maximal ideal space of L∞(G) is dense.

TL;DR: In this article, the Uhlenbeck-Ornstein process U(t) in an abstract Wiener space (H, B, i) was studied and the generalized number operator Nf(x) = −lim∈←0{E[f(U(τ ∈ξ))] − f(x)}/E[τ∈ Δ] where τxϵ is the first exit time starting at x from the ball of radius ϵ with center x, where rt(x, dy) are the transition probabilities of U

TL;DR: In this paper, it is shown that a regular ESA sequence is a boundedly complete and 1-shrinking basis for its span which is thus quasi-reflexive, and it is further shown that each unconditional IS basis gives rise to an ESA basis by means of an inversion formula.

TL;DR: In this paper, it was shown that a Banach star algebra is a C ∗ -algebra in an equivalent norm if each of its commutative closed star subalgebras is a c ∗ −algebra.

TL;DR: For a class of potentials including the Coulomb potential q = μr−1 with σ < 1 (∗) (i.e., atomic numbers Z ⩽ 137), the virial theorem (u, α · pu) = (u r(∂q∂r)u) is shown to hold, u being an eigenfunction of the operator as discussed by the authors.

TL;DR: In this paper, a topology based on order properties is defined on ∗-algebras of unbounded operators, and behaves properly with respect to the usual algebraic operations of C∗algebras.

TL;DR: For a closed densely defined operator T on a complex Hilbert space H and a spectral measure E for H of countable multiplicity q defined on a σ-algebra B over an arbitrary space Λ, this article gave three conceptually differing but equivalent answers to the question asked in the title of the paper.

TL;DR: In this article, the Radon-Nikodým property was used to show that a compact convex subset of a locally convex vector space is a simplex if and only if each point x admits a unique probability measure on the extreme points of C with barycenter x.