The publishing house
MATFYZPRESS
of the
FACULTY OF MATHEMATICS AND PHYSICS
CHARLES UNIVERSITY, PRAGUE
has published the following lecture notes:

FUNCTION SPACES
Lectures Spring School in Analysis, Paseky 1999 

FUNCTION SPACES AND
INTERPOLATION
Lectures Spring School in Analysis, Paseky 2001 

FUNCTION SPACES AND APPLICATIONS
Lectures Spring School in Analysis, Paseky 2003 

FUNCTION SPACES AND APPLICATIONS
Lectures Spring School in Analysis, Paseky 2005 

FUNCTION SPACES, INEQUALITIES AND INTERPOLATION
Lectures Spring School in Analysis, Paseky 2007 

FUNCTION SPACES, INEQUALITIES AND INTERPOLATION
Lectures Spring School in Analysis, Paseky 2009 

HARMONIC ANALYSIS
Lectures Spring School in Analysis, Paseky 2010 

FUNCTION SPACES, APPROXIMATION, INEQUALITIES AND LINEABILITY
Lectures Spring School in Analysis, Paseky 2011 

VARIATIONAL AANALYSIS AND ITS APPLICATIONS
Lectures Spring School in Analysis, Paseky 2012 

FUNCTION SPACES AND INEQUALITIES
Lectures Spring School in Analysis, Paseky 2013 

VARIATIONAL ANALYSIS AND ITS APPLICATIONS
Lectures Spring School in Analysis, Paseky, April 2015 

FUNCTION SPACES AND LINEABILITY
Lectures Spring School in Analysis, Paseky, June 2015 

MEASURE AND INTEGRAL
by Jaroslav Lukes, Jan Maly 

INTRODUCTION TO BANACH SPACES I,II
by Petr Habala, Petr Hajek, Vaclav Zizler 

Function Spaces
Lectures Spring School on Analysis
Paseky 1999
(pp. 118, ISBN 8085863391)

The book contains main lectures presented on Spring School on Analysis,
Paseky 1999.

Function Spaces and Interpolation
Lectures Spring School on Analysis
Paseky 2001
(pp. 86, ISBN 8085863669)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2001.

Function Spaces and Applications
Lectures Spring School on Analysis
Paseky 2003
(pp. 104, ISBN 8086732045)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2003.
 Lars Inge Hedberg and Yuri V. Netrusov:
An axiomatic approach to function spaces and spectral synthesis
 Igor Verbitsky: Integral inequalities and function spaces associated
with the Schroedinger operator

Function Spaces and Applications
Lectures Spring School on Analysis
Paseky 2005
(pp. 136, ISBN 8086732460)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2005.
 W. Desmond Evans: Approximation numbers of Sobolev embeddings
 Pavel Schvartsman: The Whitney extension problem and Helly's theorem

Function Spaces, Inequalities and Interpolation
Lectures Spring School on Analysis
Paseky 2007
(pp. 72, ISBN 8073780097)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2007.
 Grahame Bennett: The Classical Inequalities Revisited
 Björn Jawerth and Mario Milman: Lectures on Optimization, Image Processing and Interpolation Theory

Function Spaces, Inequalities and Interpolation
Lectures Spring School on Analysis
Paseky 2009
(pp. 146, ISBN 9788073780852)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2009.
 Anders Björn: Newtonian spaces: Firstorder Sobolev spaces on metric spaces
 Fernando Cobos: Interpolation theory and compactness
 Thierry Coulhon: Sobolev inequalities on noncompact Riemannian manifolds
 Peter A. HästE Muckenhoupt weights and variableexponent function spaces

Harmonic Analysis
Lectures Spring School on Analysis
Paseky 2010
(pp. 183, ISBN 9788073781224)

The book contains main lectures presented on Spring School on Harmonic Analysis,
Paseky 2010.
 Gerald B. Folland: The Many Faces of the Heisenberg Group
 Stéphane Jaffard: An introduction to Davenport series
 Thomas William Körner: Category and Probablistic Constructions in Harmonic Analysis

Function Spaces, Approximation, Inequalities and Lineability
Lectures Spring School on Analysis
Paseky 2011
(pp. 183, ISBN 9788073781699)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2011.
 Richard M. Aron: Linearity in nonlinear problems
 Michael Lacey: Two Weight Inequalities in Harmonic Analysis: First Results and Outstanding Challenges
 Andrei K. Lerner: The local sharp maximal function and some applications

Variational analysis and its Applications
Lectures Spring School on Analysis
Paseky 2012
(pp. 59, ISBN 9788073782047)


Function Spaces and Inequalities
Lectures Spring School on Analysis
Paseky 2013
(pp. 150, ISBN 9788073782337)

The book contains main lectures presented on Spring School on Analysis,
Paseky 2013.
 Lars Diening: Lipschitz truncation, Discrete Sobolev Spaces
 Javier Duoandikoetxea: Forty years of Muckenhoupt weights
 Carlos Perez: Singular integrals and weights: a modern introduction
 Vladimir Stepanov: Integral operators on the semiaxis: boundedness, compactness and estimates of the characteristic numbers

Variational analysis and its Applications
Lectures Spring School on Analysis
Paseky, April 2015
(pp. 220, ISBN 9788073782887)

The book contains main lectures presented on Spring School on Analysis,
Paseky, April 2015.
 Marián Fabian: Separable Reductions and Rich Families in Theory of Fréchet Subdifferentials
 Alexander Ioffe: Metric Regularity. Theory and Applications
 David Russell Luke: Numerical Variational Analysis

Function Spaces and Inequalities
Lectures Spring School on Analysis
Paseky, June 2015
(pp. 172, ISBN 9788073782917)

The book contains main lectures presented on Spring School on Analysis,
Paseky, June 2015.
 Pekka Koskela: Lectures on planar Sobolev extension domains
 Luboš Pick: Howto find the optimal partner
 Juan B. Seoane Sepúlveda: Lineability and Spaceability in Mathematics. Linearity in Nonlinear Settings

Jan Maly, Jaroslav Lukes :
Measure and Integral
(pp. 178, ISBN 8085863065)

The introductory part, where the
abstract theory of measure and integral is discussed, is followed by a
chapter on integration in locally compact spaces. This culminates with
the Riesz representation theorem. A brief introduction to measure
theory on groups (Haar measure) is appended to this chapter. The study
on integration on the real line contains the Lebesgue differentiation
theorem and the HenstockKurzweil integral. From the topics on measure
and integration on R^n, the covering theorems, differentiation of
measures, density topology and approximately continuous functions are
included. New proofs of the Rademacher and Besicovitch theorems are
presented. A part of the book is devoted to the study of the theory of
distributions, Fourier transform, approximation in function spaces and
degree theory. The presentation on the line and surface integral is
based on kdimensional measure (possibly Hausdorff measure) and
change of variables for Lipschitz surfaces. The chapter proceeds from an
elementary approach (gradient, divergence, rotation) to more advanced
one (differential forms on manifolds). The book is finished with
integration of Banach space valued functions, where the Bochner, Pettis
and Dunford integrals are discussed. Each chapter contains notes and
remarks. An ample list of references is included at the end of the
book. The text is intended for graduate and senior undergraduate
students and young researchers.
CONTENT :
 Measures and Measurable Functions
 The Lebesgue Measure
 Abstract Measures
 Measurable Functions
 Construction of Measures from Outer Measures
 Classes of Sets and Set Functions
 Signed and Complex Measures
 The Abstract Lebesgue Integral
 Integration on R
 The Abstract Lebesgue Integral
 Integrals Depending on a Parameter
 The L^p Spaces
 Product Measures and the Fubini Theorem
 Sequences of Measurable Functions
 The RadonNikodym Theorem and the Lebesgue Decomposition
 Radon Integral and Measure
 Radon Integral and Radon Outer Measure
 Radon Measures
 Riesz Representation Theorem
 Sequences of Measures
 Luzin's Theorem
 Measures on Topological Groups
 Integration on R
 Integral and Differentiation
 Functions of Finite Variation and Absolutely Continuous Functions
 Theorems on Almost Everywhere Differentiation
 Indefinite Lebesgue Integral and Absolute Continuity
 Radon Measures on R and Distribution Functions
 HenstockKurzweil Integral
 Integration on Rn
 Lebesgue Measure and Integral on Rn
 Covering Theorems
 Differentiation of Measures
 Lebesgue Density Theorem and Approximately Continuous Functions
 Lipschitz Functions
 Approximation Theorems
 Distributions
 Fourier Transform
 Change of Variable Formula and kdimensional Measures
 Change of Variable Theorem
 The Degree of a Mapping
 Hausdorff Measures
 Surface and Curve Integrals
 Integral Calculus in Vector Analysis
 Integration of Differential Forms
 Integration on Manifolds
 Vector Integration
 Measurable functions
 Vector Measures
 The Bochner Integral
 The Dunford and Pettis Integrals
 Appendix on Topology
 Bibliography and References
 A Short Guide to the Notation
 Subject Index
In TeX form available too.

Petr Habala, Petr Hajek, Vaclav Zizler :
Introduction to Banach Spaces I,II
(pp. 329, ISBN:8085863146)

The first chapters of this two volume text contain an uptodate elementary and
selfcontained introduction to basic principles and techniques in Banach
and Hilbert spaces,
spectral theory of selfadjoint compact operators and fixed points.
Besides the results that are usually presented in this area, the book
contains a study on the James boundaries and the results of Asplund, Kadets,
Lindenstrauss and Smulyan on the interplay of the differentiability of
convex functions and geometry of Banach spaces. In the chapter on locally
convex spaces, BanachDieudonne theorem, EberleinSmulyan theorem and
Choquet
representation theorem are included.
The second part of the text leads the reader to several
streams of contemporary research in Banach spaces and analysis on them.
One chapter is devoted to the use
of the Schauder basis in Banach spaces. Nonseparable Banach spaces are studied
in the chapter on weak compact generating, where basic results on
projectional resolutions of identity, Markusevic bases and
various types of compacta are discussed. The chapter on superreflexive
spaces contains Enflo's renorming theorem, the local reflexivity principle and
the results of Kadets and Gurarii  Gurarii.
The second volume of the text ends with a chapter on nonlinear analysis on
Banach spaces. It contains the Aharoni, Heinrich, Kadets, Lindenstrauss
and Mankiewicz
results on homeomorphisms and Lipschitz homeomorphisms of Banach spaces,
together with a
brief discussion on the smooth variational principle, smooth approximation
in Banach spaces and norm attaining operators. An important part of the
book is the large number of exercises. They complement the results in
chapters and are all accompanied with detailed hints for their solution.
The text is intended for graduate and senior undergraduate students and
young researchers.
CONTENT :
 Preface
 Basic Concepts in Banach Spaces
Banach spaces, subspaces, quotient spaces, Holder and Minkowski
inequalities, classical spaces c_0, l_p, L_p[0,1], C[0,1],
finitedimensional subspaces, Hilbert spaces, Riesz' lemma, separability,
orthonormal bases in Hilbert spaces. In Exercises: basic properties of Banach
spaces, unconditional convergence.
 HahnBanach Theorem, Dual Space
The HahnBanach theorem, dual space, dual operators, elementary Riesz'
representation of duals to c_0, l_p, L_p[0,1] and C[0,1]. In
Exercises: basic examples, duality, the Banach limit.
 Weak Topologies, More on the Structure of Banach
Weak topology, weak star topology, second dual, bounded sets,
BanachSteinhaus theorems, Alaoglu's theorem, Goldstine's theorem,
reflexivity, extreme points, the KreinMilman theorem, JamesSimonsGodefroy
theorems on James boundaries of sets, James' characterization of weak
compactness, the EberleinSmulyan and KreinSmulyan theorems in
separable spaces. In Exercises: basic properties of the weak and weak star
topologies, extremal structure of convex sets, dual spaces, more on
separation theorems.
 Open Mapping Theorem, More on Classical Spaces
Banach's open mapping and closed graph theorems, projections and
complementability, Auerbach bases, Sobczyk's theorem on complementability of
c_0 in separable overspaces, Phillips' theorem on noncomplementability of
c_0 in l_infty, every separable Banach space is isometric to a subspace
of C[0,1], every separable Banach space is isomorphic to a quotient of
l_1, Schur's theorem on the coincidence of weak and norm convergence of
sequences in l_1. In Exercises: subspaces, complementability, hyperplanes,
projections, isomorphisms, isometries, operators, bilinear forms.
 Differentiability of Norms and Duality
Gateaux and Frechet differentiability of norms, Smulyan's dual test,
Kadets's renorming of spaces with separable dual by Frechet differentiable
norms, the AsplundLindenstrauss result on Frechet differentiability on
dense set of convex functions on spaces with separable dual, Mazur's theorem,
Lindenstrauss' results on strongly exposed points of weakly compact sets. In
Exercises: differentiability of convex functions and extremal structure of
convex sets in classical spaces, rotundity, KadetsKlee property, Fenchel
duality, Mazur's intersection property.
 Compact Operators on Banach Spaces
Finite rank and compact operators, spectrum and resolvent, selfadjoint
operators on Hilbert spaces, spectral radius, spectral theory of compact
selfadjoint operators on Hilbert spaces, normal operators, the Fredholm
alternative, Fredholm operators, examples of integral operators. In
Exercises: examples on spectra, HilbertSchmidt operators, Lomonosov's
theorem on invariant subspaces.
 Fixed Point Property
The MarkovKakutani theorem, Banach's contraction principle, nonexpansive
mappings in Hilbert spaces, Schauder's theorems, applications to differential
equations. In Exercises: examples of fixed points, Alspach's fixedpointfree
isometry on a weakly compact set, Werner's proof of the MarkovKakutani
theorem.
 Locally Convex Spaces
The notion of a locally convex space, metrizability, normability, finite
dimensionality, separation, the bipolar theorem, the MackeyArensKatetov
theorem, the space of distributions, Choquet's representation theorem in
metrizable case, the BanachDieudonne theorem, the EberleinSmulyan
theorem, Kaplansky's theorem on countable tightness of the weak topology of a
Banach space, the BanachStone theorem. In Exercises: examples, Sobolev
spaces, the GrothendieckPtak results.
 Schauder Bases
The notion of a Schauder basis, shrinking and boundedly complete bases,
James' theorems on the characterization of reflexivity in terms of bases,
Mazur's basic sequence theorem, the KreinMilmanRutman stability result,
Pelczynski's theorems on subspaces of l_p spaces, unconditional
Schauder bases, James' theorem on containment of l_1 and c_0, Pitt's
theorem, James' space J, Khintchine's inequality, Rademacher functions in
L_p. In Exercises: examples of Hamel and Schauder bases, isomorphisms, more
on the James space.
 Weakly Compact Sets and Spaces They Generate
Weakly compactly generated spaces, the notion of an Eberlein compact, the
notion of a Markushevich's basis, AmirLindenstrauss' projectional
resolutions of the identity on weakly compactly generated spaces,
DavisFigielJohnsonPelczynski's factorization, Rosenthal's
characterization of Eberlein compacta, weakly Lindelof spaces
(PreissTalagrand), scattered compacts, the notion of a uniform Eberlein
compact and renorming of C(K) by uniformly Gateaux differentiable norms
(ArgyrosBenyaminiFarmakiStarbirdTroyanski), quasicomplements
(GurariiKadets), Polish or Czech complete balls in their weak topology
(Godefroy, Edgar, Wheeler), absolutely summing operators, Pietsch's lemma and
the DvoretzkyRogers theorem, the DunfordPettis property. In Exercises:
examples, the three space property, weakly countably determined (Vasak)
spaces, the Namioka property and other types of compacta.
 Uniform Rotundity, Finite Representability
Uniform rotundity, the modulus of rotundity, uniform Frechet
differentiability, duality, uniform convexity of L_p spaces for
p in (1,infty), Kadets's result on unconditional bases in uniformly rotund
spaces, the notion of finite representability, the local reflexivity
principle, superreflexive spaces, Enflo's renorming of superreflexive spaces,
the GurariiGurariiJames theorem on Schauder bases in superreflexive spaces.
In Exercises: examples on uniform convexity and smoothness, URED norms, the
type and cotype of Banach spaces, Stegall's results on trees in dual spaces,
the original definition of Tsirelson's space.
 Application of Smoothness in Banach Spaces
Kadets's result that all infinitedimensional separable reflexive Banach
spaces are mutually homeomorphic, Aharoni's result that every separable
Banach space is Lipschitz equivalent to a subset of c_0, the
HeinrichMankiewicz method of linearization of Lipschitz maps, the smooth
variational principle and the BishopPhelps theorem as its consequence,
Lindenstrauss' result on the density of norm attaining operators, the
BonicFrampton result on smooth approximation in separable spaces,
subdifferentiability. In Exercises: examples on the smooth variational
principle, rotundity, the AharoniLindenstrauss space, the Gorelik principle,
the Haar measure.
 References
 Index