Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
bornology; inductive limit; Fréchet space; functional calculus
bornology; inductive limit; Fréchet space; functional calculus
Summary:
We show that some unital complex commutative LF-algebra of ${\mathcal {C}}^{(\infty )}$ $\mathbb {N}$-tempered functions on $\mathbb {R}^+$ (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.
References:
[1] Bourbaki, N.: Éléments de Mathématique. Fasc. XXVII: Algèbre Commutative. Hermann, Paris (1961), French. MR 0217051 | Zbl 0205.06001
[2] Bourbaki, N.: Éléments de Mathématique. Fasc. XXXII: Théories spectrales. Hermann, Paris (1967), French. MR 0213871 | Zbl 0152.32603
[3] Buchwalter, H.: Espaces vectoriels bornologiques. Publ. Dép. Math., Lyon 2 (1965), 2-53 French. MR 0188747 | Zbl 0137.09303
[4] Ferrier, J. P.: Séminaire sur les Algèbres complètes. Lectures Notes in Mathematics 164. Berlin, Springer (1970), French. DOI 10.1007/bfb0069597 | MR 0270157 | Zbl 0203.13203
[5] Hemdaoui, M.: Approximations analytique sur les compacts de $\mathbb{C}^n$. Thèse $3^{ {ème}}$ cycle. Année universitaire (Février) 1982. Université des Sciences et Technologies. Lille 1, France French Avaible at https://ori-nuxeo.univ-lille1.fr/nuxeo/site/esupversions/1b9d01d3-5d59-496d-877d-9ca2a836b129\kern0pt
[6] Hemdaoui, M.: Calcul symbolique et l'opérateur de Laplace. Thèse Année Académique 1986-1987: ULB. Bruxelles, Belgique French Avaible at https://dipot.ulb.ac.be/dspace/bitstream/2013/213480/1/680effa8-3d2a-4225-bcb6-c0c6e156cac8.txt\kern0pt
[7] Hemdaoui, M.: An application of Mittag-Leffler lemma to the L.F algebra of $\mathcal{C}^{(\infty)}$ $\mathbb{N}$-tempered functions on $\mathbb{R}^+$. Sarajevo J. Math. 13 (2017), 61-70. DOI 10.5644/SJM.13.1.04 | MR 3666352
[8] Hogbe-Nlend, H.: Complétion, tenseurs et nucléarité en bornologie. J. Math. Pures Appl., IX. Sér. 49 (1970), 193-288 French. MR 0279557 | Zbl 0199.18001
[9] Hogbe-Nlend, H.: Theory of Bornologies and Application. Lecture Notes 213. Springer, Berlin (1971), French. DOI 10.1007/BFb0069416 | MR 0625157 | Zbl 0225.46005
[10] Hogbe-Nlend, H.: Bornologies and Functional Analysis. Introductory Course on the Theory of Duality Topology-Bornology and Its Use in Functional Analysis. North-Holland Mathematics Studies 26; Notas de Matematica 62. North Holland Publishing Company, Amsterdam (1977). DOI 10.1016/s0304-0208(08)x7105-1 | MR 0500064 | Zbl 0359.46004
[11] Hoc, Nguyen The: Croissance des coefficients spectraux et calcul fonctionnel. Thèse Année Académique 1975-1976. ULB. Bruxelles, Belgique French Avaible at https://dipot.ulb.ac.be/dspace/bitstream/2013/214383/1/62487895-bcef-4c2e-b604-8eab9d4023a7.txt\kern0pt
[12] Horvarth, J.: Topological Vector Spaces and Distributions. Vol. 1. Addison-Wesley Series in Mathematics. Addison-Wesley, Ontario (1966). MR 0205028 | Zbl 0143.15101
[13] Vasilescu, F. H.: Analytic Functional Calculus and Spectral Decompositions. Mathematics and Its Applications 1 (East European Series). D. Reidel Publishing compagny, Dordrecht (1982). MR 0690957 | Zbl 0495.47013
[14] Waelbroeck, L.: Le calcul symbolique dans les algèbres commutatives. C. R. Acad. Sci., Paris 238 (1954), 556-558 French. MR 0073950 | Zbl 0055.10704
[15] Waelbroeck, L.: Études spectrales des algèbres complètes. Mém. Cl. Sci., Collect. Octavo, Acad. R. Belg. 31 (1960), 142 pages French. MR 0117578 | Zbl 0193.10005
[16] Waelbroeck, L.: Calcul symbolique lié à la croissance de la résolvante. Rend. Sem. Mat. Fis. Milano 34 (1964), 51-72 French. DOI 10.1007/BF02923398 | MR 0170220 | Zbl 0145.16701
[17] Waelbroeck, L.: The holomorphic functional calculus and non-Banach algebras. Algebras in Analysis. Proc. Instr. Conf. and NATO Advanced Study Inst., Birmingham 1973 Academic Press, London 187-251 (1975). MR 0435847 | Zbl 0441.46041
[18] Wrobel, W.: Extension du calcul fonctionnel holomorphe et applications à l'approximation. C. R. Acad. Sci. Paris, Sér. A 275 (1972), 175-177 French. MR 0315455 | Zbl 0245.46073
Search
Partner of
