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- DescriptionRenewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in Mathematics collects the main results on the conditions for the existence of large algebraic substructures. It investigates lineability issues in a variety of areas, including real and complex analysis. After presenting basic concepts about the existence of linear structures, the book discusses lineability properties of families of functions defined on a subset of the real line as well as the lineability of special families of holomorphic (or analytic) functions defined on some domain of the complex plane. It next focuses on spaces of sequences and spaces of integrable functions before covering the phemen of universality from an algebraic point of view. The authors then describe the linear structure of the set of zeros of a polymial defined on a real or complex Banach space and explore specialized topics, such as the lineability of various families of vectors. The book concludes with an account of general techniques for discovering lineability in its diverse degrees.
- Author BiographyRichard M. Aron is a professor of mathematics at Kent State University. He is editor-in-chief of the Journal of Mathematical Analysis and Applications. He is also on the editorial boards of Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas (RACSAM) and the Mathematical Proceedings of the Royal Irish Academy. His primary research interests include functional and nonlinear analysis. He received his PhD from the University of Rochester. Luis Bernal Gonzalez is a full professor at the University of Seville. His main research interests are complex analysis, operator theory, and the interdisciplinary subject of lineability. He is the author or coauthor of more than 80 papers in these areas, many of them concerning the structure of the sets of mathematical objects. He is also a reviewer for several journals. He received his PhD in mathematics from the University of Seville. Daniel M. Pellegrino is an associate professor at the Federal University of Paraiba. He is also a researcher at the National Council for Scientific and Technological Development (CNPq) in Brazil. He is an elected affiliate member of the Brazilian Academy of Sciences and a young fellow of The World Academy of Sciences (TWAS). He received his PhD in mathematical analysis from Unicamp (State University of Sao Paulo). Juan B. Seoane Sepulveda is a professor at the Complutense University of Madrid. He is the coauthor of over 100 papers. His main research interests include real and complex analysis, operator theory, number theory, geometry of Banach spaces, and lineability. He received his first PhD from the University of Cadiz jointly with the University of Karlsruhe and his second PhD from Kent State University.
- Author(s)Daniel M. Pellegrino,Juan B. Seoane Sepulveda,Luis Bernal-Gonzalez,Richard M. Aron
- PublisherApple Academic Press Inc.
- Date of Publication12/10/2015
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleMonographs and Research Notes in Mathematics
- Series Part/Volume Number14
- Place of PublicationOakville
- Country of PublicationCanada
- ImprintApple Academic Press Inc.
- Content Note19 black & white illustrations, 2 black & white tables
- Weight612 g
- Width156 mm
- Height235 mm
- Spine23 mm
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