Elliptic resonance problems with unequal limits at infinity.
Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold
We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Embedding C(K) in B(X).
Embedding theorems for Müntz spaces
We discuss boundedness and compactness properties of the embedding , where is the closed linear span of the monomials in and is a finite positive Borel measure on the interval . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from ...
Embeddings of finite-dimensional operator spaces into the second dual
We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.
Embeddings of Sobolev spaces
Empathy theory and the Laplace transform
This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.
Employing different loss functions for the classification of images via supervised learning
Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions....
Enclosing roots of polynomial equations and their applications to iterative processes.
Enclosures and semi-analytic discretization of boundary value problems
Encore des classes de symboles
Endpoint estimates for a class of Littlewood--Paley operators with nondoubling measures.
Endpoint estimates for multilinear commutator of Marcinkiewicz operator
Endpoint estimates from restricted rearrangement inequalities.
Enflo operators of
Enlargement Procedure for Resolution of Singularities at Simple Singular Solutions of Nonlinear Equations.
Énoncé de quelques résultats sur les opérateurs intégraux singuliers dans et dans
Entire functions of order , with bounds on both axes.
Entire solutions of the abstract Cauchy problem.