'Et moi, .. Of si j'avail su comment en revenir. je One selVice mathematics has rendered the n'y semis point alll!.' human race. It has put common sense back Jules Verne when: it belongs, on the topmon shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with iL O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlineari ties abound, Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sci ences, Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. , '; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Klappentext

I. Introduction.- Terminology and notation.- Elementary facts on complex topological vector spaces.- Exercise.- A review of basic facts in the theory of distributions.- Exercises.- II. Mellin distributions and the Mellin transformation.- The Fourier and the Fourier-Mellin transformations.- Exercises.- The spaces of Mellin distributions with support in a polyinterval.- Exercises.- Operations of multiplication and differentiation in the space of Mellin distributions.- Exercises.- The Mellin transformation in the space of Mellin distributions.- Exercises.- The structure of Mellin distributions.- Exercises.- Paley-Wiener type theorems for the Mellin transformation.- Exercises.- . Mellin transforms of cut-off functions (continued).- Exercises.- . Important subspaces of Mellin distributions.- Exercises.- . The modified Cauchy transformation.- Exercises.- III. Fuchsian type singular operators.- . Fuchsian type ordinary differential operators.- Exercises.- . Elliptic Fuchsian type partial differential equations in spaces % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacI % cacaWG4bWaaSaaaeaacaWGKbaabaGaamizaiaadIhaaaGaaiykaiaa % dwhacqGH9aqpcaWGMbaaaa!3EE9!$$ P(x\frac{d}{{dx}})u = f $$.- 2. Case of a proper cone.- Exercise.- . Fuchsian type partial differential equations in spaces with continuous radial asymptotics.- Appendix. Generalized smooth functions and theory of resurgent functions of Jean Ecalle.- 1. Introduction.- 2. Generalized Taylor expansions.-3. Algebra of resurgent functions of Jean Ecalle.- 4. Applications.- List of Symbols.

Inhalt
I. Introduction.- §1. Terminology and notation.- §2. Elementary facts on complex topological vector spaces.- Exercise.- §3. A review of basic facts in the theory of distributions.- Exercises.- II. Mellin distributions and the Mellin transformation.- §4. The Fourier and the Fourier-Mellin transformations.- Exercises.- §5. The spaces of Mellin distributions with support in a polyinterval.- Exercises.- §6. Operations of multiplication and differentiation in the space of Mellin distributions.- Exercises.- §7. The Mellin transformation in the space of Mellin distributions.- Exercises.- §8. The structure of Mellin distributions.- Exercises.- §9. Paley-Wiener type theorems for the Mellin transformation.- Exercises.- §10. Mellin transforms of cut-off functions (continued).- Exercises.- §11. Important subspaces of Mellin distributions.- Exercises.- §12. The modified Cauchy transformation.- Exercises.- III. Fuchsian type singular operators.- §13. Fuchsian type ordinary differential operators.- Exercises.- §14. Elliptic Fuchsian type partial differential equations in spaces % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacI % cacaWG4bWaaSaaaeaacaWGKbaabaGaamizaiaadIhaaaGaaiykaiaa % dwhacqGH9aqpcaWGMbaaaa!3EE9!$$ P(x\frac{d}{{dx}})u = f $$.- 2. Case of a proper cone.- Exercise.- §15. Fuchsian type partial differential equations in spaces with continuous radial asymptotics.- Appendix. Generalized smooth functions and theory of resurgent functions of Jean Ecalle.- 1. Introduction.- 2. Generalized Taylor expansions.-3. Algebra of resurgent functions of Jean Ecalle.- 4. Applications.- List of Symbols.