|
|
Approximation of a non-increasing rearrangement of a function
Franců, Martin ; Pick, Luboš (advisor) ; Felcman, Jiří (referee)
The non-increasing rearrangement of a measurable real function defined on an appropriate measure space is of the enormous significance in disciplines such as theory of function spaces or interpolation theory and their applications in PDEs. Unfortunately, while it has good and widely applicable mapping properties, it is virtually impossible to calculate the non-increasing rearrangement of a concrete given function precisely. Numerical algorithms for approximation are desirable for this reason. Such method of approximation, based on interpolation by a linear spline, is presented in this thesis. In the first half of this thesis, the developed method is described, while the error estimates of the method are subject to the second part.
|
|
|
Integral operators on function spaces
Peša, Dalimil ; Pick, Luboš (advisor) ; Nekvinda, Aleš (referee)
In this thesis, we consider Lorentz-Karamata spaces with slowly varying fuc- tions and study their properties. We first provide simpler definition of slowly varying functions and derive some of their properties. We then consider Lorentz-Karamata functionals over an arbi- trary sigma-finite measure space equipped with a non-atomic measure and corre- sponding Lorentz-Karamata spaces. We characterise non-triviality of said spaces, then study when they are equivalent to a Banach function space and obtain mul- titude of conditions, either sufficient or necessary. We further study embeddings between Lorentz-Karamata spaces and provide a partial characterisation. At last, we try to describe the associate spaces of Lorentz-Karamata spaces and succeed even in some of the limiting cases. Our contribution is mainly the characterisation of non-triviality, the partial characterisation of embeddings, the description of associate spaces in some lim- iting cases and all the results concerning Lorentz-Karamata spaces with the sec- ondary parameter q smaller than one. Those results are, as far as we are aware, new. 1
|
|
|
Approximation of a non-increasing rearrangement of a function
Franců, Martin ; Pick, Luboš (advisor) ; Felcman, Jiří (referee)
The non-increasing rearrangement of a measurable real function defined on an appropriate measure space is of the enormous significance in disciplines such as theory of function spaces or interpolation theory and their applications in PDEs. Unfortunately, while it has good and widely applicable mapping properties, it is virtually impossible to calculate the non-increasing rearrangement of a concrete given function precisely. Numerical algorithms for approximation are desirable for this reason. Such method of approximation, based on interpolation by a linear spline, is presented in this thesis. In the first half of this thesis, the developed method is described, while the error estimates of the method are subject to the second part.
|
guest ::
