Related papers: On potential spaces related to Jacobi expansions

In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including…

We present a simple proof of the continuity, in the sense distributions, of the minors of the differential matrices of mappings belonging to grand Sobolev spaces. Such function spaces were introduced in connection with a problem on minimal…

A unified approach to embedding theorems for Sobolev type spaces of vector-valued functions, defined via their symmetric gradient, is proposed. The Sobolev spaces in question are built upon general rearrangement-invariant norms. Optimal…

In this paper, our primary objective is to develop the peridynamic fractional Sobolev space and establish novel BBM-type results associated with it. We also address the peridynamic fractional anisotropic $p-$Laplacian. A secondary objective…

In this paper, a new class of Sobolev spaces with kernel function satisfying a L\'evy-integrability type condition on compact Riemannian manifolds is presented. We establish the properties of separability, reflexivity, and completeness. An…

We give a notion of compatibility between a Riemannian structure and a Jacobi structure. We prove that in case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic…

Optimal embeddings for fractional Orlicz-Sobolev spaces into (generalized) Campanato spaces on the Euclidean space are exhibited. Embeddings into vanishing Campanato spaces are also characterized. Sharp embeddings into…

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green's matrix on the boundary conditions is interpreted as the set of…

We show that the space of observables of test particles carries a natural Jacobi structure which is manifestly invariant under the action of the Poincar\'{e} group. Poisson algebras may be obtained by imposing further requirements. A…

We extend in this article the classical imbedding theorems for fractional Lebesgue-Sobolev's spaces into the so-called Grand Lebesgue spaces, with sharp constant evaluation.

We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the…

We consider time fractional parabolic equations in both divergence and non-divergence form when the leading coefficients $a^{ij}$ are measurable functions of $(t,x_1)$ except for $a^{11}$ which is a measurable function of either $t$ or…

The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…

This paper describes the theory of Jacobi curves, a far reaching extension of the spaces of Jacobi fields along Riemannian geodesics, developed by Agrachev and Zelenko. Jacobi curves are curves in the Lagrangian Grassmannian of a symplectic…

The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space.…

We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a…

In this paper, we consider an extension of Jacobi's symbol, the so called rational $2^k$-th power residue symbol. In Section 3, we prove a novel generalization of Zolotarev's lemma. In Sections 4, 5 and 6, we show that several hard…

In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…

We state ready to compute dimension formulas for the spaces of Jacobi cusp forms of integral weight $k$ and integral scalar index $m$ on subgroups of $\SL$.

A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…