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24th December 2020, 10:06 AM
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 Sathyabama Institute of Science and Technology M.Sc - Mathematics SMT5202 Functional Analysis Syllabus DEPARTMENT OF MATHEMATICS SCHOOL OF SCIENCE AND HUMANITIES SMT5202 FUNCTIONAL ANALYSIS L T P CREDIT 3 1 0 4 UNIT 1: 12 Hrs Banach Space: The definition and some examples, Continuous linear transformations, The Hahn-Banach theorem. UNIT 2: 12 Hrs Banach space (continued): The natural imbedding of N of N**, The open mapping theorem, The conjugate of an operator. UNIT 3: 12 Hrs Hilbert spaces: The definition and some simple properties, Orthogonal complements, Orthonormal sets, The conjugate space H*. UNIT 4: 12 Hrs Hilbert spaces (Continued): The adjoint of an operator, self-adjoint operators, Normal and unitary, projections. UNIT 5 12 Hrs Finite Dimensional spectral theory: Matrices Determinants and the spectrum of an operator, The spectral theorem. Total No of Hours: 60 TEXT BOOK : 1. G.F.Simmons, Introduction to Topology and Modern Analysis, McGraw Hill, International Book company, 1963. UNIT I Section 46-48 UNIT II Section 49-51 UNIT III Section 52-55 UNIT IV Section 56-59 UNIT V Section 60-62 REFERENCE BOOKS: 1. Balmohan V. Limaye, Functional Analysis, Second Edition, New Age International Pvt Ltd, 1997. 2. M.Thamban Nair, Functional Analysis, A First Course, PHI, 2002 UNIVERSITY EXAM QUESTION PAPER PATTERN: Max. Marks : 70 Exam Duration : 3 Hrs Part A : 4 questions of 5 marks each – No choice - 20 marks Part B : 5 questions from each unit of internal choice, each carrying 10 marks - 50 marks   |
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