Related papers: Weighted interpolation inequalities: a perturbatio…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic…
The image of a point situated at the center of a circularly symmetric potential is a perfect circle. The perturbative effect of non-symmetrical potential terms is to displace and break the perfect circle. These 2 effects, displacement and…
We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…
Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
We prove a weighted version of the Hardy-Littlewood-Sobolev inequality for radially symmetric functions, and show that the range of admissible power weights appearing in the classical inequality due to Stein and Weiss can be improved in…
We present a perturbation analysis of the semiclassical Wigner equation which is based on the interplay between configuration and phase spaces via Wigner transform. We employ the so-called harmonic approximation of the Schrodinger…
This paper is concerned with a class of quasilinear elliptic equations involving some potentials related to the Caffarelli-Korn-Nirenberg inequality. We prove the local boundedness and H\"older continuity of weak solutions by using the…
In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field…
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. They may serve as optimized basis functions in interpolation or…
Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\langle f(\mathbf{x})\psi^2 \rangle / \langle\psi^2\rangle$, where the $\psi(\mathbf{x})$ is a linear function on input…
This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of $BMO$-type spaces. The results are formulated in a very general framework in which $BMO$ spaces are…
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
We deal with weighted Hardy-Sobolev type inequalities for functions on $\mathbb{R}^d$, $d\geq 2$. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish…
Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…
Precise theoretical predictions are a key ingredient for an accurate determination of the structure of the Langrangian of particle physics, including its free parameters, which summarizes our understanding of the fundamental interactions…