Related papers: Analysis related to all admissible type parameters…

We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, we rely on simpler functions that capture the impact of these…

We consider a hierarchy of Poisson structures defined on rational functions on the Riemann sphere. This hierarchy is originated in the theory of the integrable Camassa-Holm equation associated with the Krein's string spectral problem.…

The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points --${\bf q}_k$ and ${\bf p}_{k+1}$ or ${\bf p}_k$ and ${\bf q}_{k+1}$-- through the invariant complete…

In this paper we consider a semigroup on trigonometric expansions that will be called the Theta semigroup since its kernel is a multiple of the third Jacobi theta function. We study properties of this semigroup and prove that it is a…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…

We study the perturbative power-series expansions of the eigenvalues and eigenvectors of a general tridiagonal (Jacobi) matrix of dimension d. The(small) expansion parameters are being the entries of the two diagonals of length d-1…

A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator valued measures and their connection to a class of generalized quaternionic coherent states…

We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it…

The possibility for the Jacobi equation to admit in some cases general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them para-Jacobi polynomials. Such polynomials are used here to build seed…

In this paper we study a family of non-classical Jacobi polynomials with varying parameters of the form $\alpha_n=n+1/2$ and $\beta_n=-n-1/2$. We obtain global asymptotics for these polynomials, and use this to establish results on the…

We study Wiener-type covering lemmas, Hardy-Littlewood-type maximal functions, and convergence theorems on metric spacs. Later we specialize down to a result for the Poisson integral. We show that, in a suitably general setting, these three…

Jacobi's results on the computation of the order and of the normal forms of a differential system are translated in the formalism of differential algebra. In the quasi-regular case, we give complete proofs according to Jacobi's arguments.…

We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schr\"odinger propagator when the potential is quadratic at infinity. This construction is based on the…

We consider integral kernels for functions $f(\hat F)$ of a minimal second-order differential operator $\hat F(\nabla)$ on a curved spacetime. We show that they can be expanded in a functional series, analogous to the DeWitt expansion for…

We show that Jacobi fields along harmonic maps between suitable spaces preserve conformality, holomorphicity, real isotropy and complex isotropy to first order; this last being one of the key tools in the proof by Lemaire and the author of…

It is well known that the Jacobi operators completely determine the curvature tensor. The question of existence of a curvature tensor for given Jacobi operators naturally arises, which is considered and solved in the previous work.…

A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function $f$ on ${\mathbb R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is assumed that…

We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed…

We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show it's commutation with certain Hecke operators and use it to construct a lift of elliptic cusp forms to Hermitian Jacobi cusp forms.…