MODERN SPECTRAL THEORY
CONTENTS CHAPTER SOME SPACES OF FUNCTIONS AND DISTRIBUTIONS 11 CALCULUS ON EUCLIDEAN SPACES 12 DISTRIBUTIONS, FOURIER TRANSFORMS 13 ESTIMATES OF FUNCTIONS AND THEIR FOURIER TRANSFORMS 14 RAPIDLY DECREASING DISTRIBUTIONS CHAPTER REAL INTERPOLATION OF BANACH SPACES 21 BANACH SPACES AND LINEAR OPERATORS 22 THE K-FUNCTIONAL 23 THE MEAN AND THE TRACE METHOD 24 COMPARISON AND DUALITY OF INTERPOLATION SPACES 25 THE REITERATION THEOREM 26 INTERPOLATION OF OPERATORS 27 QUASI-LINEARIZABLE COUPLES OF B-SPACES 28 FRIEDRICHS COUPLES C0-GROUPS AND FUNCTIONAL CALCULI 31 SUBMULTIPLICATIVE FUNCTIONS AND ALGEBRAS ASSOCIATED TO THEM 32 C0-GROUPS: CONTINUITY PROPERTIES AND ELEMENTARY FUNCTIONAL CALCULUS 33 THE DISCRETE SOBOLEV SCALE ASSOCIATED TO A C0-GROUP 34 BESOV SPACES ASSOCIATED TO A C0-GROUP 35 LITTLEWOOD-PALEY ESTIMATES 36 POLYNOMIALLY BOUNDED C0-GROUPS 37 C0-GROUPS IN HILBERT SPACES SOME EXAMPLES OF C0-GROUPS 41 WEIGHTED SOBOLEV AND BESOV SPACES 42 C0-GROUPS ASSOCIATED TO VECTOR FIELDS AUTOMORPHISMS ASSOCIATED TO C0-REPRESENTATIONS 51 REGULARITY AND COMMUTATORS 52 REGULARITY OF FRACTIONAL ORDER 53 REGULARITY PRESERVING AND REGULARITY IMPROVING OPERATORS 54 THE SPACES M R S,P(RN) 55 COMMUTATOR EXPANSIONS 5A APPENDIX: DI?ERENTIABILITY PROPERTIES OF OPERATOR-VALUED FUNCTIONS UNITARY REPRESENTATIONS AND REGULARITY 61 REMARKS ON THE FUNCTIONAL CALCULUS FOR SELF-ADJOINT OPERATORS 62 REGULARITY OF SELF-ADJOINT OPERATORS WITH RESPECT TO UNITARY C0-GROUPS 63 UNITARY GROUPS IN FRIEDRICHS COUPLES 64 ESTIMATES ON ?(H1) ??(H2) 6A APPENDIX: REMARKS ON THE FUNCTIONAL CALCULUS ASSOCIATED TO W IN B(H ) THE CONJUGATE OPERATOR METHOD 71 LOCALLY SMOOTH OPERATORS AND BOUNDARY VALUES OF THE RESOLVENT 72 THE MOURRE ESTIMATE 73 THE METHOD OF DI?ERENTIAL INEQUALITIES 74 SELF-ADJOINT OPERATORS WITH A SPECTRAL GAP 75 HAMILTONIANS ASSOCIATED TO SYMMETRIC OPERATORS IN FRIEDRICHS COUPLES 76 THE LIMITING ABSORPTION PRINCIPLE FOR SOME CLASSES OF PSEUDODI?ERENTIAL OPERATORS 7A APPENDIX: THE GRONWALL LEMMA 7B APPENDIX: A COUNTEREXAMPLE OPTIMALITY OF THE RESULTS ON THE LIMITING ABSORPTION PRINCIPLE 7C APPENDIX: ASYMPTOTIC VELOCITY FOR H = H(P) AN ALGEBRAIC FRAMEWORK FOR THE MANY-BODY PROBLEM 81 SELF-ADJOINT OPERATORS A?LIATED TO C*-ALGEBRAS 82 TENSOR PRODUCTS 83 ?-FUNCTIONS IN A C*-ALGEBRA SETTING 84 GRADED C*-ALGEBRAS SPECTRAL THEORY OF N-BODY HAMILTONIANS 91 TENSORIAL FACTORIZATIONS OF H (X) 92 SEMICOMPACT OPERATORS 93 THE N-BODY ALGEBRA 94 NON-RELATIVISTIC N-BODY HAMILTONIANS 9A APPENDIX: REMARKS ON THE C 1,1 PROPERTY QUANTUM-MECHANICAL N-BODY SYSTEMS 101 CLUSTERING OF PARTICLES 102 QUANTUM-MECHANICAL N-BODY HAMILTONIANS BIBLIOGRAPHY