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The Z transformation and its application to solutions of difference equations
Hubatová, Michaela ; Opic, Bohumír (advisor) ; Johanis, Michal (referee)
This thesis uses knowledge from the introductory course of complex analysis, especially the theory of Laurent series. It provides basic information about the Z transformation and shows its mathematical applications. The text gives characterizations of exponential type sequences and defines their Z transformation. Presented theorems can be used to determine images of exponential type sequences and to find preimages of functions holomorphic at the point infinity. These theorems are given with proofs and illustrated with examples. Also some methods of the inverse tranformation are mentioned and a list of preimages of chosen rational functions holomorphic at infinity is included. In the last chapter the Z transformation is applied to solve linear difference equations. Powered by TCPDF (www.tcpdf.org)
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Analysis in Banach spaces
Pernecká, Eva ; Hájek, Petr (advisor) ; Johanis, Michal (referee) ; Godefroy, Gilles (referee)
The thesis consists of two papers and one preprint. The two papers are de- voted to the approximation properties of Lipschitz-free spaces. In the first pa- per we prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. In particular, the Lipschitz-free space over a closed subset of Rn has the bounded approximation property. We also show that the Lipschitz-free spaces over ℓ1 and over ℓn 1 admit a monotone finite-dimensional Schauder decomposition. In the second paper we improve this work and obtain even a Schauder basis in the Lipschitz-free spaces over ℓ1 and ℓn 1 . The topic of the preprint is rigidity of ℓ∞ and ℓn ∞ with respect to uniformly differentiable map- pings. Our main result is a non-linear analogy of the classical result on rigidity of ℓ∞ with respect to non-weakly compact linear operators by Rosenthal, and it generalises the theorem on non-complementability of c0 in ℓ∞ due to Phillips. 1
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Economic analysis and the Implicit Function Theorem
Solnický, Radek ; Johanis, Michal (referee) ; Pražák, Dalibor (advisor)
Nazev pracc: Vota o implicituich funkn'rh v ekonomicke analyse Autor: Radek Solnirky Pracovisto: Katrdra innteinatirke analyzy Vedouci bakalafske prace: RNDr. Prazak Dalibor, Ph.D. e-mail veclouciho: prazak@karlin.mff.cuni.cz Ahstrakt: V unioha ekonomickych modeled! popisuji'cich rovnovahy se vy- \i7.ivii popis .situaco pomoci grafu. Rovnovahu pak pferlstavuje prusecik kfi- vek- Loft'irky naslcdujc1 ota/ka. jak .se tatf) rovnovaha ziuenf, zmeniTun-li vucj.sf parametry mod(>lu. V ramci grafu jde o [)OMim nekterycli kfivek a vznik novyeh prusccikii. Z jejich pozice se UHUZUJC, v jakcni vztahu jc nova rovnovaha vzhledrm k puvothn. V tcto praci je pfcdstavena nietoda kom- parativni staticke analyzy, inatoinaticky exaktni metody, ktera zodpovkla tuto otazku be'/ nutnosti s]K)lehat se na intuitivni pojoti situacc grafein. Jo obc-nur odvo/on jejf po.stup a nasledne jc ilustrovan na nekolika pffkladecii. Kh'cova slova: ^-eta o iuiplicitni'ch funkci'ch, rcjvnovaha. produkeni funkcu, uzitkova funkcc Title: Economic Analysis and the Implicit. Function Theorem Author: Radok Solnicky Department: Department of Mathematical Analysis Supervisor: RNDr. Prazak Dalibor. Ph.D. Supervisor's e-mail address: prazak@karlin.raff.cuni.cz Abstract: In economic models describing various equilibria, graphs are used to illustrate the...
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