Showing papers in "Journal of Functional Analysis in 1981"

TL;DR: In this article, the scattering theory of a conservative nonlinear one-parameter group of operators on a Hilbert space X relative to a group of linear unitary operators is studied.

TL;DR: In this paper, the authors considered the problem of minimizing integral functionals of the form I(u) = ∝ Ω F(x, ▽ [k] u(x)) dx, where Ω ⊂ R p, u:ω → R and ▽[k]u denotes the set of all partial derivatives of u with orders ⩽k.

TL;DR: In this article, an isomorphism between the vertex and spinor representations of affine Lie algebras for types Dl(1) and Dl + 1(2) was established.

TL;DR: In this article, the exact number of solutions for semi-linear elliptic problems is computed for concave and convex nonlinear problems, based on simple eigenvalue comparison arguments.

TL;DR: In this paper, the authors established inequalities between entropy numbers and approximation numbers for operators acting between Banach spaces, and derived inequalities between eigenvalues and entropy numbers for operator acting on a Banach space.

TL;DR: In this article, a theory of stochastic calculus of variations is presented which generalizes the ordinary calculus of variation to stochastically processes and generalizations of the Euler equation and Noether's theorem are obtained.

TL;DR: In this article, a parametrization of the Dirichlet problem in smooth domains D near non-characteristic points of ∂D is presented, where a point w of D is not characteristically if one of X1, Xn, Y1, Yn is transverse to w. Characteristic points are treated in Part II.

TL;DR: In this paper, the authors generalize Arveson's extension theorem for completely positive mappings to a Hahn-Banach principle for matricial sublinear functionals with values in an injective C ∗ -algebra or an ideal in B (H ).

TL;DR: In this paper, Malliavin introduced a technique for obtaining elliptic regularity results using function space calculus, which has a great deal to recommend it and is particularly pleasing to afficionados of the so-called Brownian sheet.

TL;DR: In this paper, it was shown that several interpolation functors, including real and complex methods, are minimal or maximal extensions from a single couple of Banach spaces, and various consequences are drawn from this property.

TL;DR: In this paper, the nonlinear scattering theory was extended to Schrodinger and Klein-Gordon equations with various kinds of nonlinear terms, including some nonlocal ones, and it was applied to non-local scattering.

TL;DR: In this paper, the exact rate of divergence of the norm of e−tH as a map from L ∞ to L∞ is determined. And a number of related problems are discussed.

TL;DR: In this article, a general mathematical framework for the connection between quantum statistical mechanics and periodic stochastic processes is presented, which is applied to KMS states given by density matrices.

TL;DR: In this paper, it was shown that (I) has an infinite number of solutions for a residual set of ƒ in H − 1 (Ω), such that for many n ∈ R N there exists an open and dense subset of ǫ in H−1 (ǫ) such that (i) has n distinct solutions for such anǫ.

TL;DR: In this article, the authors give estimates for hypercontractive properties of the diffusion semigroup on compact oriented Riemannian manifold, all by way of detailed study, as in our earlier papers, of logarithmic Sobolev inequalities on the same class of manifolds.

TL;DR: In this paper, it was shown that for any T ⩾ 0, the conditional law of xt (t > 0), given B(zs,s⩽T) a C∞ density, can be shown to hold under minimal conditions on the vectors fields which define a two component diffusion and their Lie brackets.

TL;DR: In this paper, the spatial theory of von Neumann algebras has been studied in the context of non-commutative integration of J. Dixmier and I. Segal.

TL;DR: In this article, a definition of a symmetric local semigroup of (unbounded) operators P(t) (0 ⩽ t ⩾ T for some T > 0) on a Hilbert space H, which is eventually densely defined as t → 0 is given.

TL;DR: In this paper, the authors studied convex cones in a simple Lie algebra G invariant under the adjoint group G of G and found explicit algebraic presentations of such cones in all the classical hermitian symmetric Lie algebras.

TL;DR: In this article, a spectral analysis of an abstract self-adjoint operator, H, on a Hilbert space, H ac, was studied and a further refinement of H ac into the transient absolutely continuous subspace, H tac, which is the closure of those ϑ with ( ϑ, e − itH ϑ ) = O ( t − N ) for all N and the recurrent absolutely continuous subsets, H rac = H ac ∩ H tac ⊥.

TL;DR: In this paper, the irreducibility of the energy representation of the group of smooth mappings from a Riemannian manifold of dimension d ⩾ 3 into a compact semisimple Lie group is proven.

TL;DR: In this article, a linear transformation τ on J is an isometry of J onto itself if and only if there are unitary operators U and V on H such that either τ(X) = UXV or τ[X] = UXtV, where Xt denotes the transpose of X with respect to a fixed orthonormal basis of H.

TL;DR: In this article, the authors combine harmonic analysis on certain pseudo-Riemannian symmetric spaces with results on conformally invariant linear and non-linear differential equations, which gives in many cases part of the decomposition of certain representations of the conformal group of a manifold when restricted to the isometry group.

TL;DR: In this paper, a direct variational method was used to find a minimizer for the L1(IR3) problem under nearly optimal assumptions, even if the infimum is not finite.

TL;DR: In this paper, the additive functionals of several independent time-reversible Markov processes are studied and the results are useful, in particular, for investigating a certain class of Gaussian random fields which includes the free field of Euclidean quantum field theory and the so-called Brownian sheet.

TL;DR: In this paper, the authors considered the problem of characterizing the closed ideals in the commutative Banach algebras L'(w), where o is a radical weight function on [0, co), and multiplication is convolution.