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This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory. After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axioms of set...
This comprehensive book explores the intricate realm of fine potential theory. Delving into the real theory, it navigates through harmonic and subharmonic functions, addressing the famed Dirichlet problem within finely open sets of R^n. These sets are defined...
This book’s area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics. Special functions such as elliptic or automorphic functions have an algebro-geometric nature. These attributes permeate the book. The...
Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck’s Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to...
This monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth...
Brooks' Theorem (1941) is one of the most famous and fundamental theorems in graph theory – it is mentioned/treated in all general monographs on graph theory. It has sparked research in several directions. This book presents a comprehensive overview of this development...
The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series,...
This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide...
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a...
This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry.After a concise introduction to Gröbner and...
This monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 ? N ? G ? H ? 1 of finite groups, describe the irreducible representations of G by means of the structure of the group...
This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications.As in the case of other interesting quaternionic function theories, the original...
This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real...
This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a...
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz...
This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic...
The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying...
This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental...
This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by...
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject,...
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