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Besicovitch and Rado [1] and Kinney [5] proved the following result: There is a closed set E ⊂ R2 with measure zero which contains a circle of every radius. The construction of Besicovitch and Rado works in Rd: If d ≥ 3 there is a closed set E ⊂ Rd with measure zero which contains a sphere of every radius. We will give an exposition of this construction in… (More)

- Sebastian E. Ferrando, Lawrence A. Kolasa, Natasa Kovacevic
- ACM Trans. Math. Softw.
- 2002

In digital signal processing it is often advantageous to analyze a given signal using an adaptive method. The signal is approximated or represented as a superposition of "basic" waveforms chosen from a <i>dictionary</i> of such waveforms so as to best match the signal. The matching pursuit algorithm of Mallat and Zhang is such a method and is discussed in… (More)

In this paper we consider smooth analogues of operators studied in connection with pointwise convergence of the solution of the free Schrr odinger equation to the given initial data. Such operators are interesting examples of oscillatory integral operators with degenerate phase functions, and we obtain sharp L 2 ! L 2 bounds. 0. Introduction. We begin this… (More)

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