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Perfect functions of the first Baire class
Skovajsa, Břetislav ; Spurný, Jiří (advisor) ; Zajíček, Luděk (referee)
A wide class of problems in mathematical analysis can be described as searching for properties P such that for each F from a given system of mappings F between spaces K and L an arbitrary real valued function on L has the property P if and only if its composition with F also has this property. The inspiration for this text comes from [1], where the mentioned problem is examined in the form of stability of Baire classes of functions towards composition with a continuous mapping between compact topological spaces. The goal of this text will be to get acquainted with the original result, to slightly improve it on compact metric spaces, then to take a closer look at the finer structure of B1 functions and to try to find a similar kind of stability in this environment. [1] J. Lukeš, J. Malý, I. Netuka, J. Spurný, Integral representation theory: ap- plications to convexity, Banach spaces and potential theory, Walter de Gruyter (2010).
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Zobecněné obyčejné diferenciální rovnice v metrických prostorech
Skovajsa, Břetislav ; Malý, Jan (advisor) ; Pražák, Dalibor (referee)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Generalized ordinary differential equations in metric spaces
Skovajsa, Břetislav ; Malý, Jan (advisor)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Generalized ordinary differential equations in metric spaces
Skovajsa, Břetislav ; Malý, Jan (advisor)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Zobecněné obyčejné diferenciální rovnice v metrických prostorech
Skovajsa, Břetislav ; Malý, Jan (advisor) ; Pražák, Dalibor (referee)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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|
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Perfect functions of the first Baire class
Skovajsa, Břetislav ; Spurný, Jiří (advisor) ; Zajíček, Luděk (referee)
A wide class of problems in mathematical analysis can be described as searching for properties P such that for each F from a given system of mappings F between spaces K and L an arbitrary real valued function on L has the property P if and only if its composition with F also has this property. The inspiration for this text comes from [1], where the mentioned problem is examined in the form of stability of Baire classes of functions towards composition with a continuous mapping between compact topological spaces. The goal of this text will be to get acquainted with the original result, to slightly improve it on compact metric spaces, then to take a closer look at the finer structure of B1 functions and to try to find a similar kind of stability in this environment. [1] J. Lukeš, J. Malý, I. Netuka, J. Spurný, Integral representation theory: ap- plications to convexity, Banach spaces and potential theory, Walter de Gruyter (2010).
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