## Analyticity spaces, trajectory spaces, and linear mappings between them |

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### Contents

The space S | 9 |

Characterization of continuous linear mappings between the spaces | 16 |

Examples of S spaces | 22 |

5 other sections not shown

### Common terms and phrases

adjoint operators algebra analytic vector analyticity space bounded subsets characterization choice commuting self-adjoint operators compact comprises all continuous continuous iff continuous linear mappings converges absolutely Corollary cyclic defined definition makes sense denote dense Dirac's formalism distribution theory eigenfunctions eigenkets eigenvalues eigenvectors Eijndhoven elements embeddings extendable linear mappings finite number Further Graaf Hence Hilbert space Hilbert-Schmidt operator iff there exists integral converges interpretation of Dirac's introduced Kernel theorem Lie group locally convex topology mathematical matrix n-set nm nm nonnegative null sequence null set orthonormal basis Proof prove Qh(x resp satisfies Section self-adjoint operator semigroup seminorms spectral strong topology strongly subspace sufficiently small supp(p SX,A test ket Theorem Let topological structure topological tensor product topological vector space trajectory spaces TX,A uniform multiplicity unitarily equivalent unitary operators weak topology weakly convergent weighted shift zijn