Choose an application

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

The author studies high energy resonances for the operators $-Delta_{partialOmega,delta}:=-Delta delta_{partialOmega}otimes Vquad extrm{and}quad -Delta_{partialOmega,delta'}:=-Delta delta_{partialOmega}'otimes Vpartial_u$ where $Omegasubset{mathbb{R}}^{d}$ is strictly convex with smooth boundary, $V:L^{2}(partialOmega)o L^{2}(partialOmega)$ may depend on frequency, and $delta_{partialOmega}$ is the surface measure on $partialOmega$.

Potential theory (Mathematics) --- Differentiable dynamical systems. --- Potentiel, Théorie du. --- Systèmes dynamiques. --- Mathematical physics. --- Mathematical physics --- Physical mathematics --- Physics --- Mathematics

Choose an application

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

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Topological Groups. --- Potential theory (Mathematics). --- Differential equations, partial. --- Harmonic analysis. --- Functional analysis. --- Global differential geometry. --- Topological Groups, Lie Groups. --- Potential Theory. --- Partial Differential Equations. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Differential Geometry. --- Geometry, Differential --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Groups, Topological --- Continuous groups --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Partial differential equations --- Topological groups. --- Lie groups. --- Partial differential equations. --- Differential geometry. --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Lie groups --- Potential theory (Mathematics) --- Harmonic analysis --- Functional analysis

Choose an application

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

The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.

Geology --- Mathematics. --- Geomathematics --- Mathematical geology --- Differential equations, partial. --- Integral equations. --- Potential theory (Mathematics). --- Partial Differential Equations. --- Integral Equations. --- Potential Theory. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Equations, Integral --- Functional equations --- Functional analysis --- Partial differential equations --- Partial differential equations.

Choose an application

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

"In this memoir, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0, 1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0, 1]n, density of the medium is homogeneous and represented by the Lebesgue measure. Our study includes densities which are singular to the homogeneous one. We establish a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0, 1]2 and self-similar measures. We are going to show the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, we obtain diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, we introduce "protodistance"associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub- Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown"--

Potential theory (Mathematics) --- Markov processes. --- Fractals. --- Potentiel, Théorie du. --- Markov, Processus de. --- Fractales. --- Brownian motion processes. --- Mathematical analysis. --- Heat --- Processus de mouvement brownien --- Analyse mathématique --- Chaleur --- Transmission. --- transmission --- Brownian motion processes --- Mathematical analysis --- 517.1 Mathematical analysis --- Wiener processes --- Brownian movements --- Fluctuations (Physics) --- Markov processes --- Heat transfer --- Thermal transfer --- Transmission of heat --- Energy transfer --- Transmission

Choose an application

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

In 1967 Walter K. Hayman published ‘Research Problems in Function Theory’, a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as ‘Hayman's List’. This Fiftieth Anniversary Edition contains the complete ‘Hayman's List’ for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems and results needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.

Functions of complex variables. --- Differential equations, partial. --- Potential theory (Mathematics). --- Functions of a Complex Variable. --- Several Complex Variables and Analytic Spaces. --- Potential Theory. --- Complex variables --- Elliptic functions --- Functions of real variables --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Partial differential equations