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Geometric function theory. --- Functions of complex variables. --- Geometry, Differential. --- Retracts, Theory of. --- Hermitian operators. --- Fonctions, Théorie géométrique des. --- Fonctions d'une variable complexe. --- Géométrie différentielle. --- Rétractes, Théorie des. --- Opérateurs hermitiens. --- Théorie géométrique des fonctions --- Fonctions d'une variable complexe --- Géométrie différentielle --- Théorie des rétractes --- Opérateurs hermitiens --- Geometric function theory --- Functions of complex variables --- Geometry, Differential --- Retracts, Theory of --- Hermitian operators --- Operators, Hermitian --- Operators, Symmetrical --- Symmetrical operators --- Linear operators --- Topology --- Differential geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Function theory, Geometric

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In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.

Bessel functions --- Hypergeometric functions --- Geometric function theory --- Inequalities (Mathematics) --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Operations Research --- Bessel functions. --- Hypergeometric functions. --- Geometric function theory. --- Function theory, Geometric --- Functions, Hypergeometric --- Cylindrical harmonics --- Mathematics. --- Difference equations. --- Functional equations. --- Functions of complex variables. --- Functions of real variables. --- Special functions. --- Special Functions. --- Functions of a Complex Variable. --- Real Functions. --- Difference and Functional Equations. --- Special functions --- Mathematical analysis --- Equations, Functional --- Functional analysis --- Real variables --- Functions of complex variables --- Complex variables --- Elliptic functions --- Functions of real variables --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Science --- Processes, Infinite --- Transcendental functions --- Hypergeometric series --- Bessel polynomials --- Harmonic analysis --- Harmonic functions --- Functions, special.

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The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

Geometric function theory. --- Mathematics. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Functions of a Complex Variable. --- Functional Analysis. --- Dynamical Systems and Ergodic Theory. --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Math --- Science --- Function theory, Geometric --- Functions of complex variables --- Differential equations, partial. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations

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The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.

Dynamics. --- Geometric function theory. --- Geometry. --- Graph theory. --- Graphs. --- Limit theorems (Probability theory). --- Markov processes. --- Probability theory. --- Markov processes --- Graph theory --- Geometric function theory --- Limit theorems (Probability theory) --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Probabilities --- Function theory, Geometric --- Functions of complex variables --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Extremal problems --- Markov, Processus de. --- Graphes, Théorie des. --- Fonctions, Théorie géométrique des. --- Théorèmes des limites (théorie des probabilités)