Difference between revisions of "Defining operator"
From Encyclopedia of Mathematics
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| − | ''for a sequence | + | {{TEX|done}} |
| + | ''for a sequence $x=\{x_p\}$'' | ||
| − | An operator | + | 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 | + | converting the sequence $x$ to some [[Positive sequence|positive sequence]]. |
Latest revision as of 16:36, 13 November 2014
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=34485
Defining operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Defining_operator&oldid=34485
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