Browsing by Subject "convolution"

Now showing 1 - 5 of 5

Access status: Open Access ,
A general elliptic equation with intrinsic operator
(Wydawnictwa AGH, 2025) Motreanu, Dumitru
Existence and bound of a solution is established for a general elliptic equation with intrinsic operator subject to Dirichlet boundary condition. This provides a sufficient condition to the fundamental question if there is a solution belonging to a prescribed ball in the function space. An application deals with an equation involving a convolution product.
Access status: Open Access ,
A note on confidence intervals for deblurred images
(Wydawnictwa AGH, 2020) Biel, Michał; Szkutnik, Zbigniew
We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.
Access status: Open Access ,
Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
(2012) Castro, Luís P.; Saitoh, Saburou; Nguyen, Minh Tuan
This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
Access status: Restricted ,
Nierówności wagowe norm pewnych operatorów splotowych
(Data obrony: 2016-06-30) Majek, Agnieszka
Wydział Matematyki Stosowanej
Access status: Restricted ,
Postac funkcjonałów liniowo-multiplikatywnych w algebrze $L^{1}\mathbb{(R)}$
(Data obrony: 2011-07-06) Mateja, Arkadiusz
Wydział Matematyki Stosowanej