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Abstract Interpretation approximates the semantics of a program by mimicking its concrete fixpoint computation on an abstract domain $\mathbb{A}$. The abstract (post-) fixpoint computation is classically divided into two phases: the…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…
In this paper, we are concerned with the asymptotic behavior of weak solutions to certain elliptic and parabolic problems involving the fractional $p$-Laplacian in cylindrical domains that become unbounded in one direction. The nonlocal…
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…
We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…
Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding…
In the present paper we study the solvability of the Dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients which are small perturbations of given operators in rough domains beyond the…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We consider the two closely related topics of inhomogeneous problems and problems with boundary data in fractional…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
For many physical quantities, theory supplies weak- and strong-coupling expansions of the types $\sum a_n \alpha ^n$ and $ \alpha ^p\sum b_n (\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero radius of convergence. We…
We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate…
We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the…
We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.
A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral…