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Item Open Access Analytic properties of Besov spaces via Bergman projections(American Mathematical Society, 2008) Kaptanoğlu, H. T.; Üreyen, A. E.Show more We consider two-parameter Besov spaces of holomorphic functions on the unit ball of CN: We obtain various exclusions between Besov spaces of di®erent parameters using gap series. We estimate the growth near the boundary and the growth of Taylor coe±cients of functions in these spaces. We ¯nd the unique function with maximum value at each point of the ball in each Besov space. We base our proofs on Bergman projections and imbeddings between Lebesgue classes and Besov spaces. Special cases apply to the Hardy space H2, the Arveson space, the Dirichlet space, and the Bloch space.Show more Item Open Access The development of the principal genus theorem(Springer, 2007) Lemmermeyer, Franz; Goldstein, C.; Schappacher, N.; Schwermer, J.Show more Genus theory today belongs to algebraic number theory and deals with a certain part of the ideal class group of a number field that is more easily accessible than the rest. Historically, the importance of genus theory stems from the fact that it was the essential algebraic ingredient in the derivation of the classical reciprocity laws, from Gauss’s second proof, via Kummer’s contributions, all the way to Takagi’s reciprocity law for p-th power residues.Show more Item Open Access Fibre products, character sums and geometric Goppa codes(CRC Press, 1998) Stepanov, Serguei A.; Stepanov, Serguei A.; Yıldırım, Cem YalçınShow more The purpose of this paper is to construct some new families of smooth projective curves over a finite field Fq with extremely many Fq-rational points. The genus in every such family is considerably less than the number of rational points, and these two facts allow to produce sufficiently long geometric Gappa codes with very good parameters.Show more Item Open Access Hessian Tensor and standard static space-times(2008) Dobarro, F.; Ünal, Bülent; Scherfner, M.; Plaue, M.Show more In this brief survey, we will remark the interaction among the Hessian tensor on a semi-Riemannian manifold and some of the several questions in Lorentzian (and also in semi-Riemannian) geometry where this 2-covariant tensor is involved. In particular, we deal with the characterization of Killing vector fields and the study of a set of consequences of energy conditions in the framework of standard static space-times.Show more Item Open Access The Hilbert transform, rearrangements, and logarithmic determinants(Institute of Mathematics of the Polish Academy of Science, 2002) Matsaev, V.; Ostrovskii, Iossif; Sodin, M.; Zelazko, W.Show more Item Open Access On the Pontryagin-Viro form(American Mathematical Society Translations: Series 2, 2001) Degtyarev, A.Show more Item Open Access Preface(CRC Press, 1998) Stepanov, Serguei A.; Stepanov, Serguei A.; Yıldırım, Cem YalçınShow more Item Open Access Reproducing kernel kreĭn spaces(Springer Basel, 2015) Gheondea, AurelianShow more This chapter is an introduction to reproducing kernel Kre?in spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach used in this survey involves the more abstract, but very useful, concept of linearization or Kolmogorov decomposition, as well as the underlying concepts of Kre?in space induced by a selfadjoint operator and that of Kre?in space continuously embedded. The operator range feature of reproducing kernel spaces is emphasized. A careful presentation of Hermitian kernels on complex regions that point out a universality property of the Szegö kernels with respect to reproducing kernel Kre?in spaces of holomorphic functions is included. © Springer Basel 2015. All rights are reserved.Show more Item Open Access A survey of results on primes in short intervals(CRC Press, 1998) Yıldırım, Cem Yalçın; Stepanov, Serguei A.; Yıldırım, Cem YalçınShow more