Mathematica Bohemica, Vol. 142, No. 2, pp. 137-143, 2017

On the equivalence of differential operators of infinite order with constant coefficients

Yuriy Linchuk

Received January 18, 2016.   First published November 25, 2016.

Yuriy S. Linchuk, Department of Mathematical Analysis, Chernivtsi National University, 2 Kotsjubynskoho Rd., Chernivtsi, 58012, Ukraine, e-mail:

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.

Keywords: space of analytic functions; operator of differentiation of infinite order; equivalence of operators; commutant

Classification (MSC 2010): 47B38

DOI: 10.21136/MB.2016.0007-16

Full text available as PDF.

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