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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!$$P(xfrac{d}{{dx}})u = f $$.- 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.