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~Et moi, .... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aUe.· human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· sense', The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. lleaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e1re of this series.
Sommario
1. Almost periodic functions.- 1. Almost periodic functions and Bohr compactilication.- 2. Besicovitch almost periodic functions and harmonic analysis.- 3. Structure of Bohr compactifications and spaces of almost periodic functions.- 4. Stepanov almost periodic functions.- 5. Weakly almost periodic functions.- 6. Spaces of smooth almost periodic functions on Rn.- Comments.- 2. Preliminaries.- 1. Some integral inequalities.- 2. Composition operators.- Comments.- 3. Solutions of evolution variational inequalities bounded and almost periodic in time.- 1. On variational inequalities.- 2. Bounded solutions.- 3. Regularity and almost periodicity of bounded solutions.- 4. The use of compactness.- 5. Almost periodicity in the sense of Besicovitch.- 6. Singular perturbation.- 7. Some examples and additional results.- Comments.- 4. Bounded and almost periodic solutions of certain evolution equations.- 1. Abstract evolution equations.- 2. Applications.- 3. Additional results.- Comments.- 5. Problems that are almost periodic in space variables.- 1. Nonlinear elliptic equations.- 2. Almost periodic first order systems.- 3. Symmetric hyperbolic systems with monotone nonlinearity.- 4. A nonlinear Schrödinger-type equation.- Comments.- Appendix 1. On certain linear evolution equations.- Appendix 2. On certain wave equations.- Appendix 3. Open questions.- References.
