## Cordes' two-parameter spectral representation theory |

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### Contents

An Introduction | 1 |

Preliminary Results | 4 |

The TwoParameter System | 26 |

Copyright | |

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### Common terms and phrases

algebras analytic assumptions of Lemma bounded linear operator Brezis and J L Cauchy College de France commute Condition 5.1 consider constant convergence Corollary 7.2 denotes the arc dense in H eigencurves eigenvalue essentially self-adjoint estimate f G H finite dimensional follows Fractional calculus France Seminar functional G B(H G P(T G R(P H Brezis Hilbert space Id-E II(K inner product J L Lions Lemma Let f Let H multiparameter spectral theory Nonlinear partial differential norm notation o k,n obtain open interval operator in H orthogonal projection P(V T parameter partial differential equations positive definite Proof Rellich's theorem result s-lim self-adjoint in H self-adjoint operators Semigroups spectral family spectrum subspace tff G H tfu G two-parameter problem two-parameter spectral University of Strathclyde v o e