Volume 58 in the WORLD SCIENTIFIC LECTURE NOTES IN PHYSICS series.This volume constitutes a course on a number of central concepts of solid state physics, such as the classification of solids, band theory, the developments in one-electron band theory with the presence of perturbation, effective Hamilton theory, and other theories.
Volume 58 in the WORLD SCIENTIFIC LECTURE NOTES IN PHYSICS series.This volume constitutes a course on a number of central concepts of solid state phys...
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of...
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These e...
Norm inequalities relating (i) a function and two of itsderivatives and (ii) a sequence and two of its differencesare studied. Detailed elementary proofs of basicinequalities are given. These are accessible to anyone witha background of advanced calculus and a rudimentaryknowledge of the Lp and lp spaces.The classical inequalities associated with the names ofLandau, Hadamard, Hardy and Littlewood, Kolmogorov, Schoenberg and Caravetta, etc., are discussed, as well astheir discrete analogues and weighted versions. Bestconstants and the existence and nature of extremals arestudied and many open...
Norm inequalities relating (i) a function and two of itsderivatives and (ii) a sequence and two of its differencesare studied. Detailed elementary pro...
The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems discussed includes Borsuk-Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases, extensions of equivariant maps and equivariant homotopy classification, genus and G-category, elliptic boundary value problem, equivalence of p-group representations. The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology...
The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems dis...
This lecture note describes the main analytical approaches to stochastic cooling. The first is the time domain picture, in which the beam is rapidly sampled and a statistical analysis is used to describe the cooling behaviour. The second is the frequency domain picture, which is particularly useful since the observations made on the beam are mainly in this domain. This second picture is developed in detail to assess key components of modern cooling theory like mixing and signal shielding and to illustrate some of the diagnostic methods. Finally the use of a distribution function and the...
This lecture note describes the main analytical approaches to stochastic cooling. The first is the time domain picture, in which the beam is rapidly s...
The theme of this monograph is an interplay between dynamical systems and group theory. The normal subgroup structure of the automorhpism groups of such "spherically homogenous" rooted trees is investigated in detail.
The theme of this monograph is an interplay between dynamical systems and group theory. The normal subgroup structure of the automorhpism groups of su...
This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is...
This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, posit...
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases - typically in the presence of a gauge symmetry - non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the...
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the t...
Silicene and related materials are currently among the most actively studied materials, especially following the first experimental synthesis on substrates in 2012. The book then presents the atomic and electronic structure of free-standing silicene, followed by an account of the experimental realization of silicene on substrates.
Silicene and related materials are currently among the most actively studied materials, especially following the first experimental synthesis on subst...
