On scales of Sobolev spaces associated to generalized Hardy operators
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DOI: 10.1007/s00209-020-02651-0
Abstract: We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a Hormander multiplier theorem… read more here.
Keywords: associated generalized; hardy; spaces associated; scales sobolev ... See more keywords
Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials
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DOI: 10.1093/imrn/rny172
Abstract: The Painlevé-IV equation has three families of rational solutions generated by the generalized Hermite polynomials. Each family is indexed by two positive integers $m$ and $n$. These functions have applications to nonlinear wave equations, random… read more here.
Keywords: rational painlev; generalized hermite; functions associated; hermite polynomials ... See more keywords