Spectral Spaces

Spectral Spaces
Author: Max Dickmann
Publisher: Cambridge University Press
Total Pages: 652
Release: 2019-03-21
Genre: Mathematics
ISBN: 1107146720

Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.

Spectral Spaces and Hauntings

Spectral Spaces and Hauntings
Author: Christina Lee
Publisher: Taylor & Francis
Total Pages: 220
Release: 2017-02-17
Genre: Art
ISBN: 1317515021

This anthology explores the spatial dimension and politics of haunting. It considers how the ‘appearance’ of absence, emptiness and the imperceptible can indicate an overwhelming presence of something that once was, and still is, (t)here. At its core, the book asks: how and why do certain places haunt us? Drawing from a diversity of mediums, forms and disciplinary approaches, the contributors to Spectral Spaces and Hauntings illustrate the complicated ways absent presences can manifest and be registered. The case studies range from the memory sites of a terrorist attack, the lost home, a vanished mining town and abandoned airports, to the post-apocalyptic wastelands in literary fiction, the photographic and filmic surfaces where spectres materialise, and the body as a site for re-corporealising the disappeared and dead. In ruminating on the afteraffects of spectral spaces on human experience, the anthology importantly foregrounds the ethical and political imperative of engaging with ghosts and following their traces.

Spectral Analysis on Graph-like Spaces

Spectral Analysis on Graph-like Spaces
Author: Olaf Post
Publisher: Springer Science & Business Media
Total Pages: 444
Release: 2012-01-06
Genre: Mathematics
ISBN: 3642238394

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.

Introduction to Spectral Theory in Hilbert Space

Introduction to Spectral Theory in Hilbert Space
Author: Gilbert Helmberg
Publisher: Elsevier
Total Pages: 362
Release: 2014-11-28
Genre: Science
ISBN: 1483164179

North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

Spectral Theory and Analytic Geometry over Non-Archimedean Fields

Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Author: Vladimir G. Berkovich
Publisher: American Mathematical Soc.
Total Pages: 181
Release: 2012-08-02
Genre: Mathematics
ISBN: 0821890204

The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.

Real and Etale Cohomology

Real and Etale Cohomology
Author: Claus Scheiderer
Publisher: Springer
Total Pages: 300
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540487972

This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, étale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.

Formalism and Beyond

Formalism and Beyond
Author: Godehard Link
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 382
Release: 2014-10-09
Genre: Philosophy
ISBN: 161451996X

The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Advances in Rings, Modules and Factorizations

Advances in Rings, Modules and Factorizations
Author: Alberto Facchini
Publisher: Springer Nature
Total Pages: 341
Release: 2020-06-02
Genre: Mathematics
ISBN: 3030434168

Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.

Logic, Language, and Computation

Logic, Language, and Computation
Author: Nick Bezhanishvili
Publisher: Springer
Total Pages: 373
Release: 2011-07-18
Genre: Computers
ISBN: 3642223036

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 8th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2009, held in Bakuriani, Georgia, in September 2009. The 20 revised full papers included in the book were carefully reviewed and selected from numerous presentations given at the symposium. The focus of the papers is on the following topics: natural language syntax, semantics, and pragmatics; constructive, modal and algebraic logic; linguistic typology and semantic universals; logics for artificial intelligence; information retrieval, query answer systems; logic, games, and formal pragmatics; language evolution and learnability; computational social choice; historical linguistics, history of logic.

Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

Algebraic, Number Theoretic, and Topological Aspects of Ring Theory
Author: Jean-Luc Chabert
Publisher: Springer Nature
Total Pages: 473
Release: 2023-07-07
Genre: Mathematics
ISBN: 3031288475

This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 –24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.