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This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory. Rich opportunities are anticipated to extend these inequalities to analytic functions of several complex variables and solutions of partial differential equations.
Analytic functions. --- Approximation theory. --- Analytic functions --- Approximation theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Theory of approximation --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Mathematics. --- Functions of complex variables. --- Potential theory (Mathematics). --- Functions of a Complex Variable. --- Potential Theory. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Functions of complex variables --- Series, Taylor's
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Boundary value problems. --- Differential equations, Elliptic. --- Singularities (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Singularities (Mathematics) --- Boundary conditions (Differential equations) --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Geometry, Algebraic --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Differential equations, Linear --- Differential equations, Partial
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This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis. The book aims at spreading the seminal ideas of Maz'ya to a larger audience in faculties of sciences and engineering. In fact, all articles were inspired by previous works of Maz'ya in several frameworks, including classical and contemporary problems connected with boundary and initial value problems for elliptic, hyperbolic and parabolic operators, Schrödinger-type equations, mathematical theory of elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory. Maz'ya is author of more than 450 papers and 20 books. In his long career he obtained many astonishing and frequently cited results in the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, maximum principle for higher-order elliptic equations, Sobolev multipliers, approximate approximations, etc. The topics included in this volume will be particularly useful to all researchers who are interested in achieving a deeper understanding of the large expertise of Vladimir Maz'ya.
Differential equations, Partial. --- Mathematical physics. --- Differential equations, Partial --- Mathematics --- Calculus --- Physical Sciences & Mathematics --- Mathematics. --- Math --- Mathematical analysis. --- Analysis (Mathematics). --- Operator theory. --- Partial differential equations. --- Analysis. --- Partial Differential Equations. --- Operator Theory. --- Science --- Partial differential equations --- Functional analysis --- 517.1 Mathematical analysis --- Mathematical analysis --- Global analysis (Mathematics). --- Differential equations, partial. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic
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