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4 papers · 1 filter
Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type
Hugo Aimar, Ivana Gómez
We combine dyadic analysis through Haar type wavelets defined on Christ's families of generalized cubes, and Lax-Milgram theorem, in order to prove existence of Green's functions f…
Powers of distances to lower dimensional sets as Muckenhoupt weights
Hugo Aimar, Marilina Carena, Ricardo Durán +1
Let be an Ahlfors metric measure space. We give sufficient conditions on a closed set and on a real number in such a way that becomes a Muck…
Existence, uniqueness and stability of solutions of generalized Tikhonov-Phillips functionals
Gisela L. Mazzieri, Ruben D. Spies, Karina G. Temperini
The Tikhonov-Phillips method is widely used for regularizing ill-posed inverse problems mainly due to the simplicity of its formulation as an optimization problem. The use of diffe…
Global Saturation of Regularization Methods for Inverse Ill-Posed Problems
Terry Herdman, Ruben D. Spies, Karina G. Temperini
In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introdu…