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Titlebook: Extended Abstracts Fall 2019; Spaces of Analytic F Evgeny Abakumov,Anton Baranov,Joaquim Ortega-Cerdà Conference proceedings 2021 The Edito

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,A New Life of the Classical Szegő Formula,We collect several applications of a new version of the classical Szegő formula for orthogonal polynomials. The applications are concerned with the spectral theory of Krein strings, scattering theory for Dirac systems, and triangular factorizations of positive Wiener–Hopf operators.
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Shift-Invariant Spaces of Entire Functions,We study certain shift-invariant spaces of entire functions and characterize their sets of sampling and of interpolation. The results are similar to those for Paley-Wiener space. Furthermore we indicate that phase-retrieval works in these shift-invariant spaces. We mention several open problems that might be of interest for complex analysts.
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Two Problems on Homogenization in Geometry,We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map.
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Hausdorff Dimension Exceptional Set Estimates for Projections, Sections and Intersections,I shall survey old and recent results on the Hausdorff dimension of projections, plane sections and intersections with general sets. In particular, I shall discuss estimates on the Hausdorff dimension of the sets of projections, planes and orthogonal transformations for which the typical results fail.
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The Politics of the Roma in Italy and Spain, the corresponding family ., ., of Clark measures on .. For . and an inner function ., we show that the property . is directly related to the membership of an appropriate function in the de Branges–Rovnyak space ..
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