Titlebook: Analysis at Large; Dedicated to the Lif Artur Avila,Michael Th. Rassias,Yakov Sinai Book 2022 The Editor(s) (if applicable) and The Author(

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Mobile Datenerfassung in der PflegeThe goal of the present paper is to prove on assumption of the Generalized Riemann Hypothesis that each sufficiently large odd integer .. can be expressed in the form . where .., .. are Piatetski-Shapiro primes and .. is a prime with a missing digit.

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,On the Origins, Nature, and Impact of Bourgain’s Discretized Sum-Product Theorem,We discuss the origins, nature, and development of the discretized sum-product theorem, a result which Jean Bourgain viewed as one of his most significant.

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Cartan Covers and Doubling Bernstein-Type Inequalities on Analytic Subsets of ,,We prove a version of the doubling Bernstein inequalities for the trace of an analytic function of two variables on an analytic subset of .. The estimate applies to the whole analytic set in question including its singular points. The proof relies on a version of the Cartan estimate for maps in . which we establish in this work.

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,Logarithmic Quantum Dynamical Bounds for Arithmetically Defined Ergodic Schrödinger Operators with We present a method for obtaining power-logarithmic bounds on the growth of the moments of the position operator for one-dimensional ergodic Schrödinger operators. We use Bourgain’s semialgebraic method to obtain such bounds for operators with multifrequency shift or skew-shift underlying dynamics with arithmetic conditions on the parameters.

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The Ternary Goldbach Problem with a Missing Digit and Other Primes of Special Types,The goal of the present paper is to prove on assumption of the Generalized Riemann Hypothesis that each sufficiently large odd integer .. can be expressed in the form . where .., .. are Piatetski-Shapiro primes and .. is a prime with a missing digit.

Infant

A Note on Harmonious Sets,A flaw in ., Elsevier (1972), is corrected.

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