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We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…
Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary…
In this paper, some Jensen's type inequalities between quaternionic bounded selfadjoint operators on quaternionic Hilbert spaces are proved, using a log-convex function. Also, by applying a specific log-convex function, some particular…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…
We prove that, under some generic non-degeneracy assumptions, real analytic, centrally symmetric plane domains are determined by their Dirichlet (resp. Neumann) spectra. We prove that the conditions are open-dense for real analytic convex…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.
In the first part of this note, we review results concerning analytic characterization of convexity for planar sets. The second part is devoted to results valid for arbitrary $m \ge 2$.
Transparency is an essential requirement of machine learning based decision making systems that are deployed in real world. Often, transparency of a given system is achieved by providing explanations of the behavior and predictions of the…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the $\ell_1$-analysis setting. Using results from conic integral geometry, we show…
We give three proofs of the fact that a smoothly bounded, convex domain in R^n has smooth defining functions whose Hessians are non-negative definite in a neighborhood of the boundary of the domain.
We study the compactness of composition operators on the Bergman spaces of certain bounded convex domains in $\mathbb{C}^n$ with non-trivial analytic discs contained in the boundary. As a consequence we characterize that compactness of the…
We prove the existence of minimizers for functionals defined over the class of convex domains contained inside a bounded set D of R^N and with prescribed volume. Some applications are given, in particular we prove that the eigenvalues of…
The Dirac operator with MIT bag boundary condition in a bounded convex domain is shown to be always self-adjoint in the $H^1$-setting. This allows one to show that such operators appear as limit of Dirac operators with large positive mass…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…