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Full-Text Articles in Applied Mathematics
Local Characterization Of A Class Of Ruled Hypersurfaces In C2, Michael Bolt
Local Characterization Of A Class Of Ruled Hypersurfaces In C2, Michael Bolt
University Faculty Publications and Creative Works
Let M3⊂C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-hermitian part of the second fundamental form transforms under fractional linear transformation. The surfaces for which these forms are constant multiples of each other were identified in previous work, but when the constant had unit modulus there was a global requirement. Here we give a local characterization of hypersurfaces for which the constant has unit modulus.
The Kerzman–Stein Operator For Piecewise Continuously Differentiable Regions, Michael Bolt, Andrew Raich
The Kerzman–Stein Operator For Piecewise Continuously Differentiable Regions, Michael Bolt, Andrew Raich
University Faculty Publications and Creative Works
The Kerzman–Stein operator is the skew-hermitian part of the Cauchy operator defined with respect to an unweighted hermitian inner product on a rectifiable curve. If the curve is continuously differentiable, the Kerzman–Stein operator is compact on the Hilbert space of square integrable functions; when there is a corner, the operator is noncompact. Here, we give a complete description of the spectrum for a finite symmetric wedge and we show how this reveals the essential spectrum for curves that are piecewise continuously differentiable. We also give an explicit construction for a smooth curve whose Kerzman–Stein operator has large norm.