Lidé

doc. RNDr. Jaroslav Tišer, CSc.

Všechny publikace

A set of positive Gaussian measure with uniformly zero density everywhere

  • Autoři: Preiss, D., Riss, E., doc. RNDr. Jaroslav Tišer, CSc.,
  • Publikace: Journal of European Mathematical Society. 2021, 23(7), 2439-2466. ISSN 1435-9855.
  • Rok: 2021
  • DOI: 10.4171/JEMS/1058
  • Odkaz: https://doi.org/10.4171/JEMS/1058
  • Pracoviště: Katedra matematiky
  • Anotace:
    Existing negative results on invalidity of analogues of classical Density and Differentiation Theorems in infinite-dimensional spaces are considerably strengthened by a construction of a Gaussian measure gamma on a separable Hilbert space H for which the Density Theorem fails uniformly, i.e., there is a set M subset of H of positive gamma-measure such that

A criterion of Gamma-nullness and differentiability of convex and quasiconvex functions

  • DOI: 10.4064/sm227-2-5
  • Odkaz: https://doi.org/10.4064/sm227-2-5
  • Pracoviště: Katedra matematiky
  • Anotace:
    We introduce a criterion for a set to be Gamma-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Frechet differentiable is Gamma-null. Our criterion also implies a new result about Gateaux (and Hadamard) differentiability of quasiconvex functions.

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

  • Autoři: Lindenstrauss, J., Preiss, D., doc. RNDr. Jaroslav Tišer, CSc.,
  • Publikace: Princeton: Princeton University Press, 2012. Annals of Mathematics Studies. ISBN 9780691153551.
  • Rok: 2012
  • Pracoviště: Katedra matematiky
  • Anotace:
    This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.

Discovering Mathematica: A problem Solving Approach to Mathematical Analysis with Mathematica and Maple

  • Pracoviště: Katedra matematiky
  • Anotace:
    This book compares the two computer algebra programs, Maple and Mathematica used by students, mathematicians, scientists, and engineers.

Frechet Differentiability of Lipschitz Functions via Variational Principle

  • Autoři: doc. RNDr. Jaroslav Tišer, CSc., Preiss, D., Lindenstrauss, J.
  • Publikace: Journal of European Mathematical Society. 2010, 12(2), 385-412. ISSN 1435-9855.
  • Rok: 2010

How small are sigma-porous sets and why are we interested in it?

  • Pracoviště: Katedra matematiky
  • Anotace:
    A new role of sigma ideal of porous sets is investigated.

Frechet Differentiability of Lipschitz maps and Porous Sets in Banach Spaces

  • Autoři: doc. RNDr. Jaroslav Tišer, CSc., Lindenstrauss, J., Preiss, D.
  • Publikace: Banach spaces and their applications in Analysis. Berlin: Walter de Gruyter GmbH & Co. KG, 2007. pp. 111-123. ISBN 978-3-11-019449-4.
  • Rok: 2007
  • Pracoviště: Katedra matematiky
  • Anotace:
    Frechet Differentiability of Lipschitz maps and Porous Sets in Banach Spaces

A Generalised Sigma Porous Set with a Small Complement

  • Pracoviště: Katedra matematiky
  • Anotace:
    In every Banach space there is a sigma porous set such that the complement is zero on every smooth curve.

Lipschitz functions with unexpectedly large set of nondifferentiability points

  • Autoři: doc. RNDr. Jaroslav Tišer, CSc., Preiss, D., Csörnyei, M.
  • Publikace: Abstract and Applied Analysis. 2005, 2005(4), 361-373. ISSN 1085-3375.
  • Rok: 2005
  • Pracoviště: Katedra matematiky
  • Anotace:
    There is Lipschitz function in the plane such that the set of points where the derivative exist is uniformly purely unrectifiable.

Vitali Covering Theorem in Hilbert Space

Determination and Differentiation of Measures

On Hadamard Powers of Polynomials

Positivity Principle for More Concentrated Measures

On Convex Combinations of Hurwitz Polynomials

Multidimensional Discrete Signals and Systems

  • Autoři: Krajník, E., doc. RNDr. Jaroslav Tišer, CSc., Gregor, J.
  • Publikace: Workshop 95. Praha: České vysoké učení technické v Praze, 1995, pp. 31-32.
  • Rok: 1995

Points of Non-Differentiability of Typical Lipschitz Finctions

Two Unexpected Examples Concerning Differentiability of Lipschitz Functions on Banach Spaces

  • Autoři: doc. RNDr. Jaroslav Tišer, CSc., Preiss, D.
  • Publikace: Geometric Aspects of Functional Analysis. Basel: Birkhäuser, 1995. pp. 219-238. ISBN 3-7643-5207-8.
  • Rok: 1995

Points of Now-differentiability of Typical Lipschnitz Functions

ON BESICOVITCH 1/2-PROBLEM

  • Autoři: Preiss, D., doc. RNDr. Jaroslav Tišer, CSc.,
  • Publikace: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 1992, 49(part 2), 279-287. ISSN 0024-6107.
  • Rok: 1992

On Besicovitch 1/2-Problem

  • Autoři: doc. RNDr. Jaroslav Tišer, CSc., Preiss, D.
  • Publikace: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 1992,(45), 279-287. ISSN 0024-6107.
  • Rok: 1992

MEASURES IN BANACH-SPACES ARE DETERMINED BY THEIR VALUES ON BALLS

Differentation Theorem for Gaussian Measures on Hilbert-Space

  • Autoři: doc. RNDr. Jaroslav Tišer, CSc.,
  • Publikace: Transactions of the American Mathematical Society. 1988, 1988(308 (2)), 655-666. ISSN 0002-9947.
  • Rok: 1988

Differentation of Measures on Hilbert-Spaces

Za stránku zodpovídá: Ing. Mgr. Radovan Suk