| Title:
|
On the equivalence of differential operators of infinite order with constant coefficients (English) |
| Author:
|
Linchuk, Yuriy |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
142 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
137-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the conditions of equivalence of a differential operator of infinite order with constant coefficients to the operator of differentiation in one space of analytic functions. We also study the conditions of continuity of a differential operator of infinite order with variable coefficients in such space. (English) |
| Keyword:
|
space of analytic functions |
| Keyword:
|
operator of differentiation of infinite order |
| Keyword:
|
equivalence of operators |
| Keyword:
|
commutant |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 06738575 |
| idMR:
|
MR3660171 |
| DOI:
|
10.21136/MB.2016.0007-16 |
| . |
| Date available:
|
2017-05-23T09:57:35Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146748 |
| . |
| Reference:
|
[1] Delsartes, J.: Sur certaines transformations fonctionnelles rélatives aux équations linéaires aux dérivées partielles du second ordre.C. R. Acad. Sci. Paris 206 (1938), 1780-1782. Zbl 0018.40304 |
| Reference:
|
[2] Delsarte, J., Lions, J. L.: Transmutations d'opérateurs différentiels dans le domaine complexe.Comment. Math. Helv. 32 (1957), 113-128. Zbl 0080.29501, MR 0091386, 10.1007/BF02564574 |
| Reference:
|
[3] Fage, M. K.: Über die "Aquivalenz zweier gewöhnlicher linearer Differentialoperatoren mit analytischen Koeffizienten.Issled. Sovrem. Probl. Teor. Funkts. Kompleksn. Perem., IV. Vses. Konf. Mosk. Univ. (1958), 468-476 (in Russian). Zbl 0198.18701 |
| Reference:
|
[4] Fišman, K. M.: Equivalence of certain linear operators in an analytic space.Mat. Sb. (N.S.) 68 (110) (1965), 63-74 (in Russian). Zbl 0141.32103, MR 0185466 |
| Reference:
|
[5] Nagnibida, N. I., Oliĭnyk, N. P.: On the equivalence of differential operators of infinite order in analytic spaces.Math. Notes 21 (1977), 19-21. Zbl 0362.47012, MR 0448147, 10.1007/BF02317029 |
| Reference:
|
[6] Linchuk, Y. S.: Commutants of composition operators induced by a parabolic linear fractional automorphisms of the unit disk.Fract. Calc. Appl. Anal. 15 (2012), 25-33. Zbl 1310.47037, MR 2872109, 10.2478/s13540-012-0003-6 |
| Reference:
|
[7] Maldonado, M., Prada, J., Senosiain, M. J.: On differential operators of infinite order in sequence spaces.Proc. 6th Int. workshop On Group Analysis of Differential Equations and Integrable Systems, Cyprus 2012 (O. O. Vaneeva et al., eds.) Department of Mathematics and Statistics, University of Cyprus, Nicosia (2013), 142-146. Zbl 06300023, MR 3184245 |
| Reference:
|
[8] Meise, R., Vogt, D.: Introduction to Functional Analysis.Oxford Graduate Texts in Mathematics 2. The Clarendon Press, Oxford (1997). Zbl 0924.46002, MR 1483073 |
| . |
