Materias:

Materias:

Tabla de Contenidos: “…I Hilbert Spaces -- II Operators on Hilbert Space -- III Banach Spaces -- IV Locally Convex Spaces -- V Weak Topologies -- VI Linear Operators on a Banach Space -- VII Banach Algebras and Spectral Theory for Operators on a Banach Space -- VIII C*-Algebras -- IX Normal Operators on Hilbert Space -- X Unbounded Operators -- XI Fredholm Theory -- Appendix A Preliminaries -- §1. …”

Tabla de Contenidos: “…Coefficients Averaging for Functional Operators Generated by Irrational Rotation -- On the Verification of Linear Equations and the Identification of the Toeplitz-plus-Hankel Structure -- Asymmetric Factorizations of Matrix Functions on the Real Line -- On the Structure of the Square of a C 0(1) Operator -- On the Connection Between the Indices of a Block Operator Matrix and of its Determinant -- Quasi-commutativity of Entire Matrix Functions and the Continuous Analogue of the Resultant -- Double Barrier Options Under Lévy Processes -- A Local-trajectory Method and Isomorphism Theorems for Nonlocal C*-algebras -- Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves -- On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces -- Finite Sections of Band-dominated Operators with Almost Periodic Coefficients -- On the Toeplitz Operators with Piecewise Continuous Symbols on the Bergman Space -- Asymptotics of a Class of Operator Determinants…”

Tabla de Contenidos: “…Front Cover -- Many-Sorted Algebras for Deep Learning and Quantum Technology -- Copyright Page -- Dedication -- Contents -- List of figures -- Preface -- Acknowledgments -- 1 Introduction to quantum many-sorted algebras -- 1.1 Introduction to quantum many-sorted algebras -- 1.1.1 Algebraic structures -- 1.1.2 Many-sorted algebra methodology -- 1.1.3 Global field structure -- 1.1.4 Global algebraic structures in quantum and in machine learning -- 1.1.5 Specific machine learning field structure -- 1.1.6 Specific quantum field structure -- 1.1.7 Vector space as many-sorted algebra -- 1.1.8 Fundamental illustration of MSA in quantum -- 1.1.9 Time-limited signals as an inner product space -- 1.1.10 Kernel methods in real Hilbert spaces -- 1.1.11 R-Modules -- References -- 2 Basics of deep learning -- 2.1 Machine learning and data mining -- 2.2 Deep learning -- 2.3 Deep learning and relationship to quantum -- 2.4 Affine transformations for nodes within neural net -- 2.5 Global structure of neural net -- 2.6 Activation functions and cost functions for neural net -- 2.7 Classification with a single-node neural net -- 2.8 Backpropagation for neural net learning -- 2.9 Many-sorted algebra description of affine space -- 2.10 Overview of convolutional neural networks -- 2.11 Brief introduction to recurrent neural networks -- References -- 3 Basic algebras underlying quantum and NN mechanisms -- 3.1 From a vector space to an algebra -- 3.2 An algebra of time-limited signals -- 3.3 The commutant in an algebra -- 3.4 Algebra homomorphism -- 3.5 Hilbert space of wraparound digital signals -- 3.6 Many-sorted algebra description of a Banach space -- 3.7 Banach algebra as a many-sorted algebra -- 3.8 Many-sorted algebra for Banach* and C* algebra -- 3.9 Banach* algebra of wraparound digital signals -- 3.10 Complex-valued wraparound digital signals -- References…”

“…Emch has been one of the pioneers of the C-algebraic approach to quantum and classical statistical mechanics. …”

“…The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. …”