COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Adaptive regularization of convolution type equations in anisotropic spaces with fractional order of smoothness

## Adaptive regularization of convolution type equations in anisotropic spaces with fractional order of smoothnessAdd to your list(s) Download to your calendar using vCal - Burenkov, V (Cardiff University)
- Friday 14 February 2014, 09:45-10:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Inverse Problems Co-authors: Tamara Tararykova (Cardiff University (UK)), Theophile Logon (Cocody University (Cote d’Ivoir)) Under consideration are multidimensional convolution type equations with kernels whose Fourier transforms satisfy certain anisotropic conditions characterizing their behaviour at infinity. Regularized approximate solutions are constructed by using a priori information about the exact solution and the error, characterized by membership in some anisotropic Nikol’skii-Besov spaces with fractional order of smoothness: F, G respectively. The regularized solutions are defined in a way which is related to minimizing a Tikhonov smoothing functional involving the norms of the spaces F and G. Moreover, the choice of the spaces F and G is adapted to the properties of the kernel. It is important that the anisotropic smoothness parameter of the space F may be arbitrarily small and hence the a priori regularity assumption on the exact solution may be very weak. However, the regularized solutions still converge to the exact one in the appropriate sense (though, of course, the weaker are the a priori assumptions on the exact solution, the slower is the convergence). In particular, for sufficiently small smoothness parameter of the space F, the exact solution is allowed to be an unbounded function with a power singularity which is the case in some problems arising in geophysics. Estimates are obtained characterizing the smootheness of the regularized solutions and the rate of convergence of the regularized solutions to the exact one. Similar results are obtained for the case of periodic convolution type equations. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsBetty & Gordon Moore Library Events Type the title of a new list here Horizon: Bioengineering CRASSH Humanitas Lectures Department of Middle Eastern Studies Seminar Series Film screening - 3 Deewarein (Three Walls)## Other talksCoatable photovoltaics (Title t o be confirmed) Bioinformatics Modularity, criticality and evolvability of a developmental GRN Beyond crazy: Rationality, irrationality, and conspiracy theory The Deciding Factor - An afternoon talk Peak Youth: the end of the beginning Asclepiadaceae Cambridge - Corporate Finance Theory Symposium September 2017 - Day 2 TBC Atiyah Floer conjecture 'Cryptocurrency and BLOCKCHAIN – PAST, PRESENT AND FUTURE' CANCELLED DUE TO STRIKE ACTION Recent advances in understanding climate, glacier and river dynamics in high mountain Asia |