{"product_id":"9781774636664","title":"Semitopological Vector Spaces Hypernorms, Hyperseminorms, and Operators","description":"\u003ch1\u003eSemitopological Vector Spaces\u003c\/h1\u003e\u003ch2\u003eHypernorms, Hyperseminorms, and Operators\u003c\/h2\u003e\u003ch3\u003eMark Burgin\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Functional Analysis\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003eThis new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. \u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003eExploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory.\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003eTo make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of \u003cb\u003eSemitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators\u003c\/b\u003e is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader. \u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\u003cp\u003e\u003cstrong\u003eDr. Mark Burgin\u003c\/strong\u003e received his MA and PhD in mathematics from Moscow State University, which was one of the best universities in the world at that time, and Doctor of Science in logic and philosophy from the National Academy of Sciences of Ukraine. He was a Professor at the Institute of Education, Kiev; at International Solomon University, Kiev; at Kiev State University, Ukraine; and Head of the Assessment Laboratory in the Research Center of Science at the National Academy of Sciences of Ukraine. Currently he is working at University of California, Los Angeles, USA. Dr. Burgin is a member of the New York Academy of Sciences and an Honorary Professor of the Aerospace Academy of Ukraine. Dr. Burgin is also a member of the Science Advisory Committee at Science of Information Institute, Washington. Dr. Burgin is doing research, has publications, and taught courses in various areas of mathematics, artificial intelligence, computer science, information sciences, system theory, logic, psychology, social sciences, and methodology of science. He originated such theories as system theory of time, general information theory, theory of named sets, hyperprobability theory, and neoclassical analysis (in mathematics) and has made essential contributions to such fields as foundations of mathematics, theory of algorithms and computation, theory of knowledge, theory of intellectual activity, and complexity studies. He was the first to discover non-diophantine arithmetics; the first to axiomatize and build mathematical foundations for negative probability used in physics, finance, and economics; and the first to explicitly overcome the barrier posed by the Church-Turing Thesis. Dr. Burgin has authored and co-authored more than 500 papers and 21 books, including \u003ci\u003eStructural Reality\u003c\/i\u003e (2012), \u003ci\u003eTheory of Named Sets\u003c\/i\u003e (2011), \u003ci\u003eTheory of Information\u003c\/i\u003e (2010), \u003ci\u003eNeoclassical Analysis: Calculus Closer to the Real World\u003c\/i\u003e\"(2008), \u003ci\u003eSuper-recursive Algorithms\u003c\/i\u003e (2005), \u003ci\u003eOn the Nature and Essence of Mathematics\u003c\/i\u003e (1998), \u003ci\u003eIntellectual Components of Creativity\u003c\/i\u003e (1998), \u003ci\u003eFundamental Structures of Knowledge and\u003c\/i\u003e \u003ci\u003eInformation\u003c\/i\u003e (1997), \u003ci\u003eThe World of Theories and Power of Mind\u003c\/i\u003e (1992), and \u003ci\u003eAxiological Aspects of Scientific Theories\u003c\/i\u003e (1991). Dr. Burgin has also edited eight books.\u003c\/p\u003e\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e31 March 2021\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eCRC Press\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eApple Academic Press\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9781774636664\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e466\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eWeight (oz): \u003c\/td\u003e\n\u003ctd\u003e16.0\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"CRC Press","offers":[{"title":"Default Title","offer_id":63547596374156,"sku":"9781774636664","price":89.1,"currency_code":"USD","in_stock":true}],"url":"https:\/\/lateknightbooks.com\/products\/9781774636664","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}