##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## George Kyriazis

#### University of Cyprus \\ University of South Carolina

## \bf \Huge Weighted spaces of Distributions on the interval $[-1,1]$ and the unit ball

##### Abstract:

The Littlewood-Paley theory is extended to weighted spaces of
distributions on $[-1,1]$ with Jacobi weights
$
w(t)=(1-t)^\alpha(1+t)^\beta, *italic*
$
and to the unit ball $B^d$
in $R^d$ with weights $W_\mu(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$.
Almost exponentially localized polynomial elements (needlets)
$\{\varphi_\xi\}$, $\{\psi_\xi\}$ are constructed
and,
in complete analogy with the classical case on $R^d$,
it is shown that weighted Triebel-Lizorkin and Besov spaces
can be characterized by the size of the needlet coefficients
$\{\langle f,\varphi_\xi\rangle\}$
in respective sequence spaces.

Host: Dimitris Politis

### December 6, 2007

### 3:00 PM

### AP&M 6402

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