A useful algebra for functional calculus

Mohammed Hemdaoui

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 1, page 99-112
  • ISSN: 0862-7959

Abstract

top
We show that some unital complex commutative LF-algebra of 𝒞 ( ∞ ) ℕ -tempered functions on ℝ + (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

How to cite

top

Hemdaoui, Mohammed. "A useful algebra for functional calculus." Mathematica Bohemica 144.1 (2019): 99-112. <http://eudml.org/doc/294736>.

@article{Hemdaoui2019,
abstract = {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.},
author = {Hemdaoui, Mohammed},
journal = {Mathematica Bohemica},
keywords = {bornology; inductive limit; Fréchet space; functional calculus},
language = {eng},
number = {1},
pages = {99-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A useful algebra for functional calculus},
url = {http://eudml.org/doc/294736},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Hemdaoui, Mohammed
TI - A useful algebra for functional calculus
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 1
SP - 99
EP - 112
AB - 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.
LA - eng
KW - bornology; inductive limit; Fréchet space; functional calculus
UR - http://eudml.org/doc/294736
ER -

References

top
  1. Bourbaki, N., Éléments de Mathématique. Fasc. XXVII: Algèbre Commutative, Hermann, Paris (1961), French. (1961) Zbl0205.06001MR0217051
  2. Bourbaki, N., Éléments de Mathématique. Fasc. XXXII: Théories spectrales, Hermann, Paris (1967), French. (1967) Zbl0152.32603MR0213871
  3. Buchwalter, H., Espaces vectoriels bornologiques, Publ. Dép. Math., Lyon 2 (1965), 2-53 French. (1965) Zbl0137.09303MR0188747
  4. Ferrier, J. P., 10.1007/bfb0069597, Lectures Notes in Mathematics 164. Berlin, Springer (1970), French. (1970) Zbl0203.13203MR0270157DOI10.1007/bfb0069597
  5. Hemdaoui, M., Approximations analytique sur les compacts de ℂ n . Thèse 3 è m e 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. 
  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. 
  7. Hemdaoui, M., 10.5644/SJM.13.1.04, Sarajevo J. Math. 13 (2017), 61-70. (2017) MR3666352DOI10.5644/SJM.13.1.04
  8. Hogbe-Nlend, H., Complétion, tenseurs et nucléarité en bornologie, J. Math. Pures Appl., IX. Sér. 49 (1970), 193-288 French. (1970) Zbl0199.18001MR0279557
  9. Hogbe-Nlend, H., 10.1007/BFb0069416, Lecture Notes 213. Springer, Berlin (1971), French. (1971) Zbl0225.46005MR0625157DOI10.1007/BFb0069416
  10. Hogbe-Nlend, H., 10.1016/s0304-0208(08)x7105-1, North-Holland Mathematics Studies 26; Notas de Matematica 62. North Holland Publishing Company, Amsterdam (1977). (1977) Zbl0359.46004MR0500064DOI10.1016/s0304-0208(08)x7105-1
  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. 
  12. Horvarth, J., Topological Vector Spaces and Distributions. Vol. 1, Addison-Wesley Series in Mathematics. Addison-Wesley, Ontario (1966). (1966) Zbl0143.15101MR0205028
  13. Vasilescu, F. H., Analytic Functional Calculus and Spectral Decompositions, Mathematics and Its Applications 1 (East European Series). D. Reidel Publishing compagny, Dordrecht (1982). (1982) Zbl0495.47013MR0690957
  14. Waelbroeck, L., Le calcul symbolique dans les algèbres commutatives, C. R. Acad. Sci., Paris 238 (1954), 556-558 French. (1954) Zbl0055.10704MR0073950
  15. Waelbroeck, L., Études spectrales des algèbres complètes, Mém. Cl. Sci., Collect. Octavo, Acad. R. Belg. 31 (1960), 142 pages French. (1960) Zbl0193.10005MR0117578
  16. Waelbroeck, L., 10.1007/BF02923398, Rend. Sem. Mat. Fis. Milano 34 (1964), 51-72 French. (1964) Zbl0145.16701MR0170220DOI10.1007/BF02923398
  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). (1975) Zbl0441.46041MR0435847
  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. (1972) Zbl0245.46073MR0315455

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.