 -classification 3
-manifold (for T) 146
-operational calculus (on W) 2 6 146
-operator 4
B*-algebra 8
Baire class 15
Banach generalized limit 9
Basic algebra 1
Bernstein theorem 54
Binomial series 166
Binomial vector 165
Bochner criterion 23
Boundary group 3
Calderon — Zygmund covering lemma 55
Carlson condition 40
Commutant 27
Compact operator 66
Convolution operator 3
Core (for a closed operator) 113
Derivation 25
distribution 24
Exponential type 38
Gauss — Weierstrass semigroup 107
Gelfand transform 27
Generalized spectral measure (on W) 139
Generalized spectral operator 174
Group of operators 5
Hille — Yosida theorem 154
Infinitesimal generator 82
Invariant mean 9
Jordan decomposition 4 74
Jordan manifold ( -Jordan manifold) 143
Lerch's theorem 166
Local semigroup 164
Local spectrum 74
Marcinkiewicz' interpolation theorem 52
Maximal ideal space 27
Nilpotent 13
Nilpotent part 130
Noerlund function 88
Operational calculus 1 6
| Orliecz — Banach — Pettis theorem 136
Paley — Wiener — Schwartz theorem 24
Quasi-nilpotent 13
Quasi-nilpotent equivalent 74
Radical part 74
Rapidly decreasing function 49
Regular semigroup 38
Representation 6
Resolution of the identity 73 143
Resolvent 18
Resolvent, equation 160
Resolvent, set 19
Riemann — Liouville operator 59
Riemann — Liouville semigroup 61
Riesz representation theorem 124
Scalar part 74
Schwartz space ( ) 49
Semi simplicity manifold 148
Single-valued extension property 74
Singular -operator 5 123
Singular functional 126
Singular representation 126
Spectral local semigroup 164
Spectral measure (spectral measure on W) 73
Spectral operator 4 73
Spectral operator of scalar type 4 73
Spectral operator of scalar type, unbounded 155
Spectral operator of type n 74
Spectral pseudo-metric 30
Spectral radius 27
Stone — Weierstrass theorem 139
STR (Stieltjes Transform Representation) theorem 159
Strong type (k, k) 53
Tempered distribution 24 49
Three-lines theorem 43
Tietze extension theorem 8
Volterra commutation relation 25
Volterra element 25 30
Weak representation 22
Weak type (k, k) 53
Weakly compact operator 123
Widder differential operator 157
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