We compute the Szegö kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in Cn for Grassmannian manifolds of higher ranks. In particular they provide an infinite family of smoothly bounded strictly ...

In this paper, we address non-Euclidean geometrical aspects of the Schur and Levinson–Szegö algorithms. We first show that the Lobachevski geometry is, by construction, one natural geometrical environment of these algorithms, since they necessarily make use of automorphisms of the unit disk. We next consider the algorithms in the particular context of their application to linear prediction. The...

Monogenic orthogonal polynomials over 3D prolate spheroids were previously introduced and shown to have some remarkable properties. In particular, the underlying functions take values in the quaternions (identified with R), and are generally assumed to be nullsolutions of the well known Moisil-Théodoresco system. In this paper, we show that these polynomial functions play an important role in d...

Abstract For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, logarithmic capacity $c_{\beta }$, and analytic $c_{B}$ satisfy inequality chain $\pi K \geq c^2_{\beta } c^2_B$. Moreover, equality holds at a single point between two of three quantities if only $X$ is biholomorphic to disk possibly less relatively closed polar set. We extend by showing that $c_{B}^2 \pi v^{-1}(X)$ ...

In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫ 2π 0 f(eiθ)ω(θ)dθ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type ∑n j=1 λjf(xj) with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions ω(θ) related to th...

In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems VΦ(x), i.e., polynomialVandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n2) computational procedure. We present numer...

We study relations between two fundamental constructions associated to vector bundles on a smooth complex projective curve: the theta function (a section of a line bundle on the moduli space of vector bundles) and the Szegö kernel (a section of a vector bundle on the square of the curve). Two types of relations are demonstrated. First, we establish a higher–rank version of the prime form, descr...

We prove the Fekete-Szegö Theorem with splitting conditions for adelic sets on a smooth, connected algebraic curve defined over a number field.

In this paper, we find Fekete-Szegö bounds for a generalized class M q (γ, φ). Also, we discuss some remarkable results.

We study the regularity properties of generalized solutions of the EulerLagrange equation of a functional involving capacity and perimeter, related to a conjecture of Pólya and Szegö.