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Gauss–Manin connections for $p$ -adic families of nearly overconvergent modular forms

Robert Harron; Liang Xiao — 2014

Annales de l’institut Fourier

We interpolate the Gauss–Manin connection in $p$ -adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type $r$ to the space of nearly overconvergent modular forms of type $r + 1$ with $p$ -adic weight shifted by $2$ . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank groups.

Hybrid steepest-descent methods for solving variational inequalities governed by boundedly Lipschitzian and strongly monotone operators.

He, Songnian; Liang, Xiao-Lan — 2010

Fixed Point Theory and Applications [electronic only]

A note on the perturbed trapezoid inequality.

Cheng, Xiao-Liang; Sun, Jie — 2002

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Efficient and effective total variation image super-resolution: a preconditioned operator splitting approach.

Huang, Li-Li; Xiao, Liang; Wei, Zhi-Hui — 2011

Mathematical Problems in Engineering

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