Slant Hankel operators

Arora, Subhash Chander, Batra, Ruchika, and Singh, M. P.. "Slant Hankel operators." Archivum Mathematicum 042.2 (2006): 125-133. <http://eudml.org/doc/249783>.

@article{Arora2006,
abstract = {In this paper the notion of slant Hankel operator $K_\varphi $, with symbol $\varphi $ in $L^\infty $, on the space $L^2(\{\mathbb \{T\}\})$, $\{\mathbb \{T\}\}$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis $\lbrace z^i : i \in \{\mathbb \{Z\}\} \rbrace $ of the space $L^2$ is given by $\langle \alpha _\{ij\}\rangle = \langle a_\{-2i-j\}\rangle $, where $\sum \limits _\{i=-\infty \}^\{\infty \}a_i z^i$ is the Fourier expansion of $\varphi $. Some algebraic properties such as the norm, compactness of the operator $K_\varphi $ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible symbol $\varphi $, the spectrum of $K_\varphi $ contains a closed disc.},
author = {Arora, Subhash Chander, Batra, Ruchika, Singh, M. P.},
journal = {Archivum Mathematicum},
keywords = {Hankel operators; slant Hankel operators; slant Toeplitz operators; Hankel operators; slant Hankel operators; slant Toeplitz operators},
language = {eng},
number = {2},
pages = {125-133},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Slant Hankel operators},
url = {http://eudml.org/doc/249783},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Arora, Subhash Chander
AU - Batra, Ruchika
AU - Singh, M. P.
TI - Slant Hankel operators
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 2
SP - 125
EP - 133
AB - In this paper the notion of slant Hankel operator $K_\varphi $, with symbol $\varphi $ in $L^\infty $, on the space $L^2({\mathbb {T}})$, ${\mathbb {T}}$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis $\lbrace z^i : i \in {\mathbb {Z}} \rbrace $ of the space $L^2$ is given by $\langle \alpha _{ij}\rangle = \langle a_{-2i-j}\rangle $, where $\sum \limits _{i=-\infty }^{\infty }a_i z^i$ is the Fourier expansion of $\varphi $. Some algebraic properties such as the norm, compactness of the operator $K_\varphi $ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible symbol $\varphi $, the spectrum of $K_\varphi $ contains a closed disc.
LA - eng
KW - Hankel operators; slant Hankel operators; slant Toeplitz operators; Hankel operators; slant Hankel operators; slant Toeplitz operators
UR - http://eudml.org/doc/249783
ER -