Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Covers articles on the areas of calculus of variations, control theory, measure theory, functional analysis, differential equations, integralequations, optimization and mathematical programming. Also covers topics related to nonsmooth analysis, generalized differentiability, and set-valued functions.

Convex functions --- Functional analysis --- Convex functions. --- Functional analysis. --- Convexe functies. --- Functions, Convex --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.

Convex functions. --- Gamma functions. --- Functions, Convex --- Functions of real variables --- Functions, Gamma --- Transcendental functions --- Difference Equation --- Higher Order Convexity --- Bohr-Mollerup's Theorem --- Principal Indefinite Sums --- Gauss' Limit --- Euler Product Form --- Raabe's Formula --- Binet's Function --- Stirling's Formula --- Euler's Infinite Product --- Euler's Reflection Formula --- Weierstrass' Infinite Product --- Gauss Multiplication Formula --- Euler's Constant --- Gamma Function --- Polygamma Functions --- Hurwitz Zeta Function --- Generalized Stieltjes Constants

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

Mathematics. --- Computer graphics. --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- Differential geometry. --- Physics. --- Differential Geometry. --- Functions of a Complex Variable. --- Dynamical Systems and Ergodic Theory. --- Computer Graphics. --- Numerical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Differential geometry --- Complex variables --- Dynamical systems --- Kinetics --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Math --- Ergodic transformations --- Physical sciences --- Dynamics --- Elliptic functions --- Functions of real variables --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Science --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Digital techniques --- Global differential geometry. --- Differentiable dynamical systems. --- Numerical and Computational Physics, Simulation. --- Geometry, Differential --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differential Geometry