National Repository of Grey Literature 49 records found  1 - 10nextend  jump to record: Search took 0.00 seconds. 
Choquet Theory and Dirichlet Problem
Omasta, Eduard ; Lukeš, Jaroslav (advisor) ; Brzezina, Miroslav (referee) ; Medková, Dagmar (referee)
In our dissertation we deal with the space H(K) of harmonic functions on a compact space in classical and abstract potential theory. Initially, we prove several equivalent characteristics of this space in classical potential theory. The internal characterization, which describes H(K) as a subspace of those continuous functions on a compact space K which are finely harmonic on the fine interior of K, is then used as the definition of H(K) in abstract potential theory. Further we concentrate on the solution of the Dirichlet problem for open and compact sets mainly with regards to its relation to subclasses of Baire class one functions. The results, proved at first in classical potential theory, are later generalized to abstract potential theory. With a use of more elemen- tary tools we initially prove these results in harmonic spaces with the axiom of dominance and, subsequently, using stronger tools we generalize them to harmonic spaces with the axiom of polarity. We engage also in a more abstract problem of approximation by differen- ces of lower semicontinuous functions in a more general context of binormal topological spaces.
Extremal points of convex sets and applications
Zitko, Martin ; Lukeš, Jaroslav (advisor) ; Veselý, Jiří (referee)
The thesis consists of two sections, the theoretical and the practical one. Theoretical part deals with 1. convex analysis, its important theorems including those concerning extreme points of convex sets, and also 2. mathematical solutions of fair division problems. It is shown whether and in what way are these areas related. The practical part of the work follows on results of the previous one with various exercises. Attempts have been made so as no theoretical knowledge is required to understand the formulation of the exercises.
Orthogonality in Banach spaces
Mašková, Alice ; Lukeš, Jaroslav (advisor) ; Milota, Jaroslav (referee)
In the present work we study properties of orthogonality in Hilbert spaces and possibilities of extending definition to more general type of spaces, Banach spaces. We concentrate mostly on Birkhoff-James orthogonality and investigate, which properties of Hilbert space orthogonality are still valid for Banach spaces, otherwise we provide counter-examples. As the orthogonality is generally not symmetric, we have to distinguish between right and left properties. We use Birkhoff-James orthogonality to characterize smooth and strictly convex Banach spaces. Then we study properties of Hilbert space orthogonal projection and its generalizations for Banach spaces.We study projections of norm equal one and minimal projections.
Geometric linear and nonlinear problems of function spaces
Petráček, Petr ; Lukeš, Jaroslav (advisor) ; Aron, Richard M. (referee) ; Bobok, Jozef (referee)
Název práce: Geometrické lineární a nelineární problémy prostor· funkcí Autor: Petr Petráček Katedra: Katedra matematické analýzy 'kolitel: prof. RNDr. Jaroslav Lukeš, DrSc., Katedra matematické analýzy Abstrakt: Tato práce sestává ze čtyř vědeckých článk·. lánky prezentované v prvních dvou kapitolách se věnují teorii reálných a komplexních L1-preduál·. lánky prezentované v třetí a čtvrté kapitole jsou věnovány problematice line- ability a algebrability podmnožin reálných funkcí a měr. V Kapitole 1 předsta- vujeme charakterizaci komplexních L1-preduál· pomocí komplexního barycent- rického zobrazení. Tato charakterizace je přirozeným rozšířením charakterizace reálných L1 preduál· pocházející od Bednara a Laceyho. V Kapitole 2 odpoví- dáme na otázku položenou Laceym v roce 1973. Dokazujeme přitom existenci kompaktního prostoru K a uzavřeného podprostoru H ⊂ C(K) obsahujícího kon- stantní funkce, pro který platí ∂HK = K, H je maximální vzhledem k ∂HK a H není L1-preduál. V Kapitole 3 se věnujeme lineabilitě množin nikde mono- tonních znaménkových Radonových měr na Rd . Konkrétně dokazujeme existence vektorového prostoru dimenze c jehož každý nenulový prvek je nikde monotonní míra absolutně spojitá vzhledem k d-rozměrné Lebesgueově míře. Nadto dokazu- jeme, že existuje takový lineární prostor, který je hustý...
Variations of Banach fix point theorem
Pošta, Petr ; Hušek, Miroslav (advisor) ; Lukeš, Jaroslav (referee)
\azev prace: Yariaee Banachovy vety o pevnem bode Autor: Potr Posta Katecha (ustav): Katedra malematieke analy/y Vedouci bakalarske pn'uo: prof. R.NDr. Miroslav Husek. DrSr. e-mail vedouciho: nihnsek'fika.rlin.mff.cuni.c/ Abstrakt: V predlozene pra.ci studujcmo rozlicno dusledky a /ohccnfjiii Bana- chovy vrty o pcvnrni hodr. V prvni Oasli sliulujciin' diislcdky klasickrlio Bana- cliDva prhiripu kuiitrakcc: posloiipnosti kunlraktivnicli zo)j]'ax,(ini, ru/.iie variact1 podnn'iiky koiit.rakt.iviiost.i xobra/cni. pffkladv pou/.iti v Ranacliovych prostorodi. diskrrl.ni prinrip koiilrakcc (Filriilxn'^uva a Jachyinskrho veiv.r) a tit.a/ku ckviva.- Icncc diskrutniYh vet .s Baiiachovou \vtou. V druhr casli jsou nastinriiy moxnr prfstupy k zobrcuc'-iii liaiiachovy vely: jako ph'klady jsuu dokazany ruzne vrty o pevuriu liodr (autory jsou Edrlstcin, Bailey. Civir, Kirk a dalsf), ktr.n'1 xoheciiuji Banachovii vOlu. Kh'cova sluva: Bauacliova vela u kunt.ra.kci. konl.iakcc, prvny bod, /obc'dinnr kon- Title: Variations of Bauarh iix point tluMirrin Author: Potr I'ost.a Do]>artim'iit.: Dopart.mont of iMa.lhonia.tica.l Analysis Suporvisor: prof. RNDr. Miroslav Ilvisck. DrSc. Su]>ervisor's c-niail addrcsw: Abstract: In the prosrnt \\ork wo study various consequences and generalizations of Bana.ch tixc-d point tlieor(nii. In...
Some results in convexity and in Banach space theory
Kraus, Michal ; Lukeš, Jaroslav (advisor) ; Kalenda, Ondřej (referee) ; Smith, Richard (referee)
This thesis consists of four research papers. In the first paper we construct nonmetrizable compact convex sets with pathological sets of simpliciality, show- ing that the properties of the set of simpliciality known in the metrizable case do not hold without the assumption of metrizability. In the second paper we construct an example concerning remotal sets, answering thus a question of Martín and Rao, and present a new proof of the fact that in every infinite- dimensional Banach space there exists a closed convex bounded set which is not remotal. The third paper is a study of the relations between polynomials on Banach spaces and linear identities. We investigate under which conditions a linear identity is satisfied only by polynomials, and describe the space of poly- nomials satisfying such linear identity. In the last paper we study the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper Matuszewska-Orlicz indices. 1

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See also: similar author names
3 LUKEŠ, Jaroslav
1 Lukeš, J.
12 Lukeš, Jakub
7 Lukeš, Jan
9 Lukeš, Jiří
2 Lukeš, Julius
1 Lukeš, Jáchym
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