Overview

'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.

Full Product Details

Author:   Zofia Szmydt ,  B. Ziemian
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1992
Volume:   56
Dimensions:   Width: 16.00cm , Height: 1.30cm , Length: 24.00cm
Weight:   0.391kg
ISBN:  

9789401050692

ISBN 10:   9401050694
Pages:   222
Publication Date:   26 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

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