Parameter dependence of solutions of partial differential equations in spaces of real analytic functions

Proceedings of the American Mathematical Society

Volumn 129, Issue 2, 2001, Pages 495-503

  Bonet, José ^a,b   Domański, Pawel ^a,b  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

Author keywords

Fr chet space; Lb space; Linear partial differential operator; Parameter dependence of solutions; Space of real analytic functions; Surjectivity of convolution operators; Vector valued real analytic functions

Indexed keywords

EID: 23044524948     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-00-05867-6     Document Type: Article

References (43)

1. A. Alexiewicz, W. Orlicz, On analytic vector-valued functions of a real variable, Studio. Math. 12 (1951), 108-111. MR 13:250b
2. K. D. Bierstedt, An introduction to locally convex inductive limits, in: Functional Analysis and its Applications, H. Hogbe-Nlend (ed.), World Sci., Singapore 1988, pp. 35-133. MR 90a:46004
3. J. Bochnak, J. Siciak, Analytic functions in topological vector spaces, Studia Math. 39 (1971), 77-111. MR 47:2365
4. J. Bonet, P. Domański, Real analytic curves in Fréchet spaces and their duals, Mh. Math. 126 (1998), 13-36. MR 99i:46032
5. R. Braun, Surjectivity of partial differential operators on Gevrey classes, in: Functional Analysis, Proc. of the First International Workshop held at Trier University, S. Dierolf, P. Domański, S. Dineen (eds.), Walter de Gruyter, Berlin 1996, pp. 69-80. MR 98b:35028
6. R. Braun, R. Meise, D. Vogt, Applications of the projective limit functor to convolution and partial differential equations, in: Advances in the Theory of Fréchet Spaces, T. Terzioǧlu (ed.), Kluwer, Dordrecht 1989, pp. 29-46. MR 92b:46119
7. N, Math. Nach. 168 (1994), 19-54. MR 95g:35004
8. 1 X = 0, Mich. Math. J. 44 (1997), 149-156. MR 98c:46162
9. E. De Giorgi, L. Cattabriga, Una dimostrazione diretta dell'esistenza di soluzioni analitiche nol piano reale di equazioni a derivate parziali a coefficienti costanti, Boll. Un. Mat. Ital. 4 (1971), 1015-1027. MR 52:3702
10. B. Gramsch, Inversion von Fredholmfunktionen bei stetiger und holomorpher Abhängigkeit von Parametern, Math. Ann. 214 (1975), 95-147. MR 52:8977
11. B. Gramsch, W. Kaballo, Spectral theory for Fredholm functions, in: Functional Analysis: Surveys and Recent Results II, K. D. Bierstedt, B. Fuchssteiner (eds.), North-Holland, Amsterdam 1980, pp. 319-342. MR 81d:47008
12. A. Grothendieck, Sur certains espaces de functions holomorphes, I, II, J. Reine Angew. Math. 192 (1953), 35-64, 77-95. MR 15:963b
13. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955). MR 17:763c
14. L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Inventiones Math. 21 (1973), 151-182. MR 49:817
15. L. Hörmander, An Introduction to Complex Analysis in Several Variables, 2nd ed., North-Holland, Amsterdam 1979.
16. H. Jarchow, Locally Convex Spaces, B. G. Teubner, Stuttgart 1981. MR 83h:46008
17. S. Krantz, H. R. Parks, A Primer of Real Analytic Functions, Birkhäuser, Basel 1992. MR 93j:26013
18. G. Köthe, Topological Vector Spaces I and II, Springer, Berlin 1969 and 1979. MR 40:1750; MR 81g:46001
19. A. Kriegl, P. W. Michor, The convenient setting for real analytic mappings, Acta Math. 165 (1990), 105-159. MR 92a:58009
20. A. Kriegl, P. W. Michor, The Convenient Setting of Global Analysis, American Mathematical Society, Providence 1997. MR 98i:58015
21. J. Krone, D. Vogt, The splitting relation for Köthe spaces, Math. Z. 190 (1985), 387-400. MR 86m:46009
22. M. Langenbruch, Continuous linear right inverses for convolution operators in spaces of real analytic functions, Studio. Math. 110 (1994), 65-82. MR 95f:46061
23. M. Langenbruch, Hyperfunction fundamental solutions of surjective convolution operators on real analytic functions, J. Funct. Anal. 131 (1995), 78-93. MR 97h:35004
24. J. Leiterer, Banach coherent analytic Predict sheaves, Math. Nachr. 85 (1978), 91-109. MR 80b:32026
25. F. Mantlik, Partial differential operators depending analytically on a parameter, Ann. Inst. Fourier (Grenoble) 41 (1991), 577-599. MR 92m:35026
26. F. Mantlik, Fundamental solutions or hypoelliptic differential operators depending analytically on a parameter, Trans. Amer. Math. Soc. 334 (1992), 245-257. MR 93a:35031
27. A. Martineau, Sur les fonctionelles analytiques et la transformation de Fourier-Borel, J. Analyse Math. 11 (1963), 1-164.
28. A. Martineau, Sur la topologie des espaces de fonctions holomorphes, Math. Ann. 163 (1966), 62-88. MR 32:8109
29. R. Meise, Sequence space representations for (DFN)-algebras of entire functions modulo closed ideal, J. Reine. Angew. Math. 363 (1985), 59-95. MR 87c:46033
30. R. Meise, D. Vogt, Introduction to Functional Analysis, Clarendon Press, Oxford 1997. MR 98g:46001
31. P. Perez-Carreras, J. Bonet, Barrelled Locally Convex Spaces, North-Holland, Amsterdam 1987. MR 88j:46003
32. H. G. Tillmann, Randverteilungen analytischer Funktionen und Distributionen, Math. Z. 59 (1953), 61-83. MR 15:211a
33. D. Vogt, Charakterisierung der Unterräume eines nuklearen stabilen Potenzreihenraumes von endlichem Typ, Studia Math. 71 (1982), 251-270. MR 84d:46010
34. D. Vogt, On-the solvability of P(D)f = g for vector valued functions, RIMS Kokyoroku 508 (1983), 168-181.
35. D. Vogt, Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. Reine Angew. Math. 345 (1983), 182-200. MR 85h:46007
36. D. Vogt, Some results on continuous linear maps between Fréchet spaces, in: Functional Analysis: Surveys and Recent Results III, K. D. Bierstedt, B. Fuchssteiner (eds.), North-Holland, Amsterdam 1984, pp. 349-381. MR 86i:46075
37. D. Vogt, On two classes of (F)-spaces, Arch. Math. 45 (1985), 255-266. MR 87h:46012
38. 1(E, F) for Predict spaces, Studio. Math. 85 (1987), 163-197. MR 89a:46146
39. D. Vogt, Lectures on projective spectra of DF-spaces, Seminar lectures, AG Funktionalanalysis, Düsseldorf/Wuppertal 1987.
40. D. Vogt, Topics on projective spectra of LB-spaces, in: Advances in the Theory of Fréchet Spaces, T. Terzioǧlu (ed.), Kluwer, Dordrecht 1989, pp. 11-27. MR 93b:46011
41. J. Wengenroth, Acyclic inductive spectra of Fréchet spaces, Studio. Math. 120 (1996), 247-258. MR 97m:46006
42. G. Wiechert, Dualitäts- und Strukturtheorie der Kerne linearer Differentialoperatoren, Dissertation Wuppertal (1982).
43. V. P. Zaharjuta, Spaces of analytic functions and complex potential theory, in: Linear Topological Spaces and Complex Analysis 1, A. Aytuna (ed.), METU-TÜB. ITAK, Ankara 1994, pp. 74-146.