We consider the problem of L1 (un)boundedness for a wide class orthogonal projections, including Bergman projections on domains in complex manifolds and Szegö abstract CR manifolds.

In order to characterise the C∗ -algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in C, we compute its principal symbol. We show then that the Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral. Mathematics Subject Classification (2000). Primary 32A25; Secondary 47L15, 47G30.

In this paper, we investigate some new Pólya-Szegö type integral inequalities involving the Riemann-Liouville fractional integral operator, and use them to prove some fractional integral inequalities of Chebyshev type, concerning the integral of the product of two functions and the product of two integrals. Certain special cases are also considered. Finally, examples for constructing the boundi...

This work is in a stream (see e.g. [4], [8], [10], [11], [7]) initiated by a paper of Killip and Simon [9], an earlier paper [5] also should be mentioned here. Using methods of Functional Analysis and the classical Szegö Theorem we prove sum rule identities in a very general form. Then, we apply the result to obtain new asymptotics for orthonormal polynomials.

Abstract. In this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order b, using a linear multiplier differential operator D λ,μf(z). In this paper, for these classes the Fekete–Szegö problem is completely solved. Various new special cases of our results are also pointed out.

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szegö curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.