Concept
Compact operator on Hilbert space
Related publications (47)
The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
2021Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case
We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along traject ...
2021On compact representations of Voronoi cells of lattices
Matthias Schymura, Christoph Hunkenschröder
In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...
SPRINGER HEIDELBERG2020Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections
We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We rst investigate regularized algorithms adapted to a projection operator on a closed subspace ...
2020Sparse-RS: a versatile framework for query-efficient sparse black-box adversarial attacks
Nicolas Henri Bernard Flammarion, Maksym Andriushchenko, Francesco Croce
A large body of research has focused on adversarial attacks which require to modify all input features with small l2- or l∞-norms. In this paper we instead focus on query-efficient sparse attacks in the black-box setting. Our versatile framework, Sparse-RS ...
2020A Generalized Representer Theorem for Hilbert Space - Valued Functions
Colin Neil Jones, Sanket Sanjay Diwale
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space - valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence ...
2019Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings
The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...
2019On compact representations of Voronoi cells of lattices
Matthias Schymura, Christoph Hunkenschröder
In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...
SPRINGER INTERNATIONAL PUBLISHING AG2018Stochastic Forward-Douglas-Rachford Splitting for Monotone Inclusions
Volkan Cevher, Alp Yurtsever, Cong Bang Vu
We propose a stochastic Forward-Douglas-Rachford Splitting framework for finding a zero point of the sum of three maximally monotone operators in real separable Hilbert space, where one of the operators is cocoercive. We characterize the rate of convergenc ...
Springer International Publishing2018