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Multilinear Operator Integrals
This book provides a comprehensive treatment of multilinear operator integral techniques. The exposition is structured to be suitable for a course on methods and applications of multilinear operator integrals and also as a research aid. The ideas and contributions to the field are surveyed and up-to-date results and methods are presented. Most practical constructions of multiple operator integrals are included along with fundamental technical results and major applications to smoothness properties of operator functions (Lipschitz and Hölder continuity, differentiability), approximation of operator functions, spectral shift functions, spectral flow in the setting of noncommutative geometry, quantum differentiability, and differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more involved, technical proofs are outlined and supplemented with references. Selected open problems in the field are also presented.
Index Theory for Locally Compact Noncommutative Geometries
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
Advances in Noncommutative Geometry
This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
Singular Traces
This book is the first complete study and monograph dedicated to singular traces. The text mathematically formalises the study of traces in a self contained theory of functional analysis. Extensive notes will treat the historical development. The final section will contain the most complete and concise treatment known of the integration half of Connes' quantum calculus. Singular traces are traces on ideals of compact operators that vanish on the subideal of finite rank operators. Singular traces feature in A. Connes' interpretation of noncommutative residues. Particularly the Dixmier trace,which generalises the restricted Adler-Manin-Wodzicki residue of pseudo-differential operators and play...
Operator Theory in Different Settings and Related Applications
This book provides a selection of reports and survey articles on the latest research in the area of single and multivariable operator theory and related fields. The latter include singular integral equations, ordinary and partial differential equations, complex analysis, numerical linear algebra, and real algebraic geometry – all of which were among the topics presented at the 26th International Workshop in Operator Theory and its Applications, held in Tbilisi, Georgia, in the summer of 2015. Moreover, the volume includes three special commemorative articles. One of them is dedicated to the memory of Leiba Rodman, another to Murray Marshall, and a third to Boris Khvedelidze, an outstanding Georgian mathematician and one of the founding fathers of the theory of singular integral equations. The book will be of interest to a broad range of mathematicians, from graduate students to researchers, whose primary interests lie in operator theory, complex analysis and applications, as well as specialists in mathematical physics.
Studia mathematica
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Divine Proportions
"... introduces a remarkable new approach to trigonometry and Euclidean geometry, with dramatic implications for mathematics teaching, industrial applications and the direction of mathematical research in geometry" -- p. vii.
The Wonder Book of Geometry
Following in the footsteps of his bestselling The Calculus Story, David Acheson offers a highly illustrated tour of geometry, from ancient Greece to the present day, packed with elegant deductions and wide applications. And along the way, he uncovers some of the loveliest surprises in mathematics. Book jacket.
Adverbs and Adverbial Constructions in Old Anatolian Turkish
The objective of this work is to define and establish the class of adverbs in Old Anatolian Turkish (OAT) as a solid grammatical category. In this work, adverbs and adverbials are taken in a wider scope, and the phrasal and syntactic adverbial constructions such as word groups, converbs and adverbial clauses are analyzed for that purpose. Adverbs are treated as a syntactic phenomenon and all analyses are carried out on syntactic contexts in examples of full sentences and sentence groups. In this work, the aim is to answer the following questions in OAT: to show what the functions and functional variations of adverbs are in the sentence, to show what the structures and the structural variations of adverbs are, to define what the meanings of the adverbs in OAT as a grammatical category are by examining the lexical, morphological and syntactic elements in the sentence.
Stochastic Processes
Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
