This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.
Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory.
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
Drawing on the authors' research work from the last ten years, Mathematical Inequalities: A Perspective gives readers a different viewpoint of the field.
Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs.
Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries.
This book makes a significant inroad into the unexpectedly difficult question of existence of Frechet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces.
A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics.
Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms.
Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations.
The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation.
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways.
The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability.
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures.
The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics.
In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.
Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering.
Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis.
A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.
This book is a comprehensive and time-tested guide to the mathematical theory of Fourier series and boundary value problems, with a strong emphasis on engineering applications.
In order to study discrete Abelian groups with wide range applications, the use of classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups is required.
Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years.
In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type.
Stochastic analysis is a field of mathematical research having numerous interactions with other domains of mathematics such as partial differential equations, riemannian path spaces, dynamical systems, optimization.
In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies.
A step-by-step illustrated introduction to the astounding mathematics of symmetryThis lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry.
