JournalsprimsVol. 45, No. 2pp. 569–599

Resolution of Operator Singularities via the Mixed-Variable Method

  • Sheng-Ming Ma

    Beihang University, Beijing, China
Resolution of Operator Singularities via the Mixed-Variable Method cover
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Abstract

This paper applies a modern method of singularity resolution in algebraic geometry to resolving singularities of integral operators in Fourier analysis. This is achieved by introducing a method of mixed variables that is equivalent to changing coordinates for integral operators. We decompose the integral operator into dyadic pieces via monomial transforms and the mixed-variable method so as to obtain its sharp estimates on different domains. These sharp estimates can be written in an elegant form in terms of continued fractions.

Cite this article

Sheng-Ming Ma, Resolution of Operator Singularities via the Mixed-Variable Method. Publ. Res. Inst. Math. Sci. 45 (2009), no. 2, pp. 569–599

DOI 10.2977/PRIMS/1241553130