On the equivalence of differential operators of infinite order with constant coefficients
Mathematica Bohemica (2017)
- Volume: 142, Issue: 2, page 137-143
- ISSN: 0862-7959
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topLinchuk, Yuriy. "On the equivalence of differential operators of infinite order with constant coefficients." Mathematica Bohemica 142.2 (2017): 137-143. <http://eudml.org/doc/288111>.
@article{Linchuk2017,
abstract = {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.},
author = {Linchuk, Yuriy},
journal = {Mathematica Bohemica},
keywords = {space of analytic functions; operator of differentiation of infinite order; equivalence of operators; commutant},
language = {eng},
number = {2},
pages = {137-143},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the equivalence of differential operators of infinite order with constant coefficients},
url = {http://eudml.org/doc/288111},
volume = {142},
year = {2017},
}
TY - JOUR
AU - Linchuk, Yuriy
TI - On the equivalence of differential operators of infinite order with constant coefficients
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 2
SP - 137
EP - 143
AB - 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.
LA - eng
KW - space of analytic functions; operator of differentiation of infinite order; equivalence of operators; commutant
UR - http://eudml.org/doc/288111
ER -
References
top- 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. (1938) Zbl0018.40304
- Delsarte, J., Lions, J. L., 10.1007/BF02564574, Comment. Math. Helv. 32 (1957), 113-128. (1957) Zbl0080.29501MR0091386DOI10.1007/BF02564574
- 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). (1958) Zbl0198.18701
- Fišman, K. M., Equivalence of certain linear operators in an analytic space, Mat. Sb. (N.S.) 68 (110) (1965), 63-74 (in Russian). (1965) Zbl0141.32103MR0185466
- Nagnibida, N. I., Oliĭnyk, N. P., 10.1007/BF02317029, Math. Notes 21 (1977), 19-21. (1977) Zbl0362.47012MR0448147DOI10.1007/BF02317029
- Linchuk, Y. S., 10.2478/s13540-012-0003-6, Fract. Calc. Appl. Anal. 15 (2012), 25-33. (2012) Zbl1310.47037MR2872109DOI10.2478/s13540-012-0003-6
- 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. (2013) Zbl06300023MR3184245
- Meise, R., Vogt, D., Introduction to Functional Analysis, Oxford Graduate Texts in Mathematics 2. The Clarendon Press, Oxford (1997). (1997) Zbl0924.46002MR1483073
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