相关论文: Kolmogorov widths of anisotropic Sobolev classes
Second-order automorphic forms are similar to the usual automorphic forms but have a weaker automorphy condition. We answer a question of Zagier and find the dimensions of spaces of holomorphic, even weight, second-order forms. We also…
We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term…
Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v^v such manifolds of volume at most v, considered up to…
We compute the lengths of two particular cases of (possibly non-unital) composition algebras, namely, standard composition algebras and Okubo algebras over an arbitrary field $\mathbb{F}$. These results finish the complete description of…
The research monograph expounds the foundation of a new theory of parabolic initial-boundary-value problems in scales of generalized anisotropic Sobolev spaces. These scales are calibrated essentially more finely with the help of a function…
We study volumes of sections of convex origin-symmetric bodies in $\mathbb{R}% ^{n}$ induced by orthonormal systems on probability spaces. The approach is based on volume estimates of \ John-L\"{o}wner ellipsoids and expectations of norms…
In this note we compute the threshold regularity for meromorphic continuation of the Pollicott--Ruelle resolvent of an Anosov flow as an operator on anisotropic Sobolev spaces, in the setting of lifts to general vector bundles. These…
This paper aims at characterizing the approximability of bounded sets in the range of nonlinear operators in Banach spaces by finite-dimensional linear varieties. In particular, the class of operators we consider includes the endpoint maps…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets…
We expand the ranges of permissible values of $n$ ($n\in\mathbb{N}$) for which Poisson kernels $P_{q,\beta}(t)=\sum\limits_{k=1}^{\infty}q^k\cos\left(kt-\dfrac{\beta\pi}{2}\right)$, ${q\in(0,1)}$, $\beta\in\mathbb{R}$, satisfy Kushpel's…
We study the embeddings of (homogeneous and inhomogeneous) anisotropic Besov spaces associated to an expansive matrix $A$ into Sobolev spaces, with focus on the influence of $A$ on the embedding behaviour. For a large range of parameters,…
We consider the family of integral operators $(K_{\alpha}f)(x)$ from $L^p[0,1]$ to $L^q[0,1]$ given by $$(K_{\alpha}f)(x)=\int_0^1(1-xy)^{\alpha -1}\,f(y)\,\operatorname{d}\!y, \qquad 0<\alpha<1.$$ The main objective is to find upper bounds…
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
We investigate two types of characterizations for anisotropic Sobolev and BV spaces. In particular, we establish anisotropic versions of the Bourgain-Brezis-Mironescu formula, including the magnetic case both for Sobolev and BV functions.
We introduce a novel framework for embedding anisotropic variable exponent Sobolev spaces into spaces of anisotropic variable exponent H\"{o}lder-continuous functions within rectangular domains. We establish a foundational approach to…
We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on the number of lattice points of these minimal polygons.
In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove Hardy-type inequalities to obtain Sobolev embeddings and use…
Exact order estimates are obtained of the best $m$-term trigonometric approximations of the Nikol'skii-Besov classes $B^r_{p, \theta}$ of periodic functions of one and many variables in the space $B_{q,1}$. In the univariate case ($d=1$),…
This paper considers the Lorentz space with mixed norm of periodic functions of many variables and of the generalized Nikol'skii -- Besov classes. Estimates for the order of approximation of the generalized Nikol'skii -- Besov classes by…