| 000 | 02538cam a2200289 i 4500 | ||
|---|---|---|---|
| 001 | 135872 | ||
| 003 | ISI Library, Kolkata | ||
| 005 | 20150616114855.0 | ||
| 008 | 140630t20142014riu b 001 0 eng | ||
| 020 | _a9781470416973 (hbk.: acidfree paper) | ||
| 040 | _aISI Library | ||
| 082 |
_a510MS _223 _bAm512 |
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| 100 | 1 | _aKaliuzhnyi-Verbovetskyi, Dmitry S. | |
| 245 | 1 | 0 |
_aFoundations of free noncommutative function theory / _cDmitry S. Kaliuzhnyi-Verbovetskyi and Victor Vinnikov. |
| 260 |
_aProvidence : _bAmerican Mathematical Society, _cc2014. |
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| 300 |
_avi, 183 p. ; _c26 cm. |
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| 490 | 0 |
_aMathematical surveys and monographs ; _vv 199. |
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| 504 | _aIncludes bibliographical references (pages 175-179) and index. | ||
| 505 | 0 | _a1. Introduction-- 2. NC functions and their difference-differential calculus-- 3. Higher order nc functions and their difference-differential calculus-- 4. The Taylor-Taylor formula-- 5. NC functions on nilpotent matrices-- 6. NC polynomials vs. polynomials in matrix entries-- 7. NC analyticity and convergence of TT series-- 9. Convergence of nc power series-- 9. Direct summands extensions of nc sets and nc functions (Some) earlier work on nc functions-- Appendix A. Similarity invariant envelopes and extension of nc functions-- Bibliography-- Index. | |
| 520 | _aThis book is developed by a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is dimensionless matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, quantum control. | ||
| 650 | 0 | _aFunctional analysis. | |
| 650 | 0 | _aNoncommutative algebras. | |
| 650 | 0 | _aNoncommutative function spaces. | |
| 650 | 7 | _aNonassociative rings and algebras -- General nonassociative rings -- Free algebras. | |
| 700 | 1 | _aVinnikov, Victor. | |
| 942 |
_2ddc _cBK |
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| 999 |
_c419033 _d419033 |
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