Related papers: Translating auxiliary symmetries between Schottky …
We present an improved form of the algorithm for constructing Jacobi rotations. This is simultaneously a more accurate code for finding the eigenvalues and eigenvectors of a real symmetric 2x2 matrix.
We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders express as principal value integrals against kernels having…
We study how the spectrum of a Jacobi operator changes when this operator is modified by a certain finite rank perturbation. The operator corresponds to an infinite mass-spring system and the perturbation is obtained by modifying one…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…
A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of solutions are characterized. Such families are very general,…
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order…
Recent progress in self-supervised representation learning has resulted in models that are capable of extracting image features that are not only effective at encoding image level, but also pixel-level, semantics. These features have been…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
Our primary objective is to study Pitt-type inequalities on Riemannian symmetric spaces $\mathbb{X}$ of noncompact type, as well as within the framework of Jacobi analysis. Inspired by the spectral gap of the Laplacian on $\mathbb{X}$, we…
In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear naturally when applying reciprocal transformations to Hamiltonian…
In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil…
The concept of an adapted homology basis for a prime order conformal automorphism of a compact Riemann surface extends to arbitrary finite groups of conformal automorphisms. Here we compute some examples of adapted homology bases for some…
Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…