## A Functional Analytic Approach to the Linear Transport Equation |

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### Contents

Introduction | 1 |

The operator A | 17 |

The spectrum of the operator A y The dispersion function | 26 |

4 other sections not shown

### Common terms and phrases

9 Lip 9 Lip(I According to lemma Application Banach algebra Banach space boundary bounded linear operator bounded map bounded operators bounded projection chapter closed subspace consequence continuous functions contour Corollary corresponding decomposition derive det(E-K dispersion function eigenvalues Equation 1.1 equation 8.4 exp(xv F and F func function defined function f given half-space Hence Hilbert space Holder condition Holder-continuous functions holomorphic semigroup inequality initial value problem inner product integral interval inverse Lebesgue measure Let f linear functional linear isomorphism linear space lip N Lip(N map F map from Lip medium Moreover multiplication operator N_,a N+,a number of neutrons obtain operator norm polynomials Proof properties relation remark respectively right-hand side satisfy a uniform self-adjoint solution of 8.4 solution of equation solved spectrum tion transformation F Transport Theory unique solution variable vector space yields zero