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Defining operator

From Encyclopedia of Mathematics
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for a sequence $x=\{x_p\}$

An operator $M$ in a space of sequences having the form

$$(Mx)_p=\sum_{-l}^{+l}m_jx_{p-j};$$

$$m_j=\overline{m_{-j}},\quad\sum_{-l}^{+l}m_j\lambda^j\leq0,\quad|\lambda|=1;$$

converting the sequence $x$ to some positive sequence.

How to Cite This Entry:
Defining operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Defining_operator&oldid=11763
This article was adapted from an original article by N.K. Nikol'skiiB.S. Pavlov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article