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Search: All articles in the CMB digital archive with keyword boundedness

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1. CMB 2004 (vol 47 pp. 540)

Jain, Pankaj; Jain, Pawan K.; Gupta, Babita
Compactness of Hardy-Type Operators over Star-Shaped Regions in $\mathbb{R}^N$
We study a compactness property of the operators between weighted Lebesgue spaces that average a function over certain domains involving a star-shaped region. The cases covered are (i) when the average is taken over a difference of two dilations of a star-shaped region in $\RR^N$, and (ii) when the average is taken over all dilations of star-shaped regions in $\RR^N$. These cases include, respectively, the average over annuli and the average over balls centered at origin.

Keywords:Hardy operator, Hardy-Steklov operator, compactness, boundedness, star-shaped regions
Categories:46E35, 26D10

2. CMB 1998 (vol 41 pp. 49)

Harrison, K. J.; Ward, J. A.; Eaton, L-J.
Stability of weighted darma filters
We study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case.

Keywords:Difference equations, adaptive $\DARMA$ filters, weighted shifts,, stability and boundedness, automatic continuity
Categories:47A62, 47B37, 93D25, 42A85, 47N70

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