@book{AckermannAhlgrimmApelojgetal.2018, author = {Ackermann, Peter and Ahlgrimm, Frederik and Apelojg, Benjamin and B{\"o}rnert-Ringleb, Moritz and Borowski, Andreas and Ehlert, Antje and Eichler, Constanze and Frohn, Julia and Gehrmann, Marie-Luise and Gerlach, Erin and Goetz, Ilka and Goral, Johanna and Gronostaj, Anna and Grubert, Jana and G{\"u}lery{\"u}z, Burak and Hacke, Alexander and Heck, Sebastian and Hermanns, Jolanda and Hochmuth, J{\"o}rg and Jennek, Julia and Jostes, Brigitte and Jurczok, Anne and Kleemann, Katrin and Kortenkamp, Ulrich and Krauskopf, Karsten and K{\"u}choll, Denise and Kulawiak, Pawel R. and Lauterbach, Wolfgang and Lazarides, Rebecca and Linka, Tim and L{\"o}weke, Sebastian and Lohse-Bossenz, Hendrik and Maar, Verena and Nowak, Anna and Ratzlaff, Olaf and Reitz-Koncebovski, Karen and Rother, Stefanie and Scherreiks, Lynn and Schroeder, Christoph and Schwalbe, Anja and Schwill, Andreas and Tosch, Frank and Vock, Miriam and Wagner, Luisa and Westphal, Andrea and Wilbert, J{\"u}rgen}, title = {PSI-Potsdam}, series = {Potsdamer Beitr{\"a}ge zur Lehrerbildung und Bildungsforschung}, journal = {Potsdamer Beitr{\"a}ge zur Lehrerbildung und Bildungsforschung}, number = {1}, editor = {Borowski, Andreas and Ehlert, Antje and Prechtl, Helmut}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-442-5}, issn = {2626-3556}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-414542}, publisher = {Universit{\"a}t Potsdam}, pages = {354}, year = {2018}, abstract = {In Brandenburg kommt der Universit{\"a}t Potsdam eine besondere Rolle zu: Sie ist die einzige, an der zuk{\"u}nftige Lehrerinnen und Lehrer die erste Phase ihres Werdegangs - das Lehramtsstudium - absolvieren k{\"o}nnen. Vor diesem Hintergrund wurde bereits kurz nach der Gr{\"u}ndung im Jahr 1991 das „Potsdamer Modell der Lehrerbildung" entwickelt. Dieses Modell strebt fortlaufend eine enge Verzahnung von Theorie und Praxis {\"u}ber das gesamte Studium hinweg an und bindet hierf{\"u}r die schulpraktischen Studienanteile in besonderer Weise ein. Eine erneute St{\"a}rkung erfuhr die Lehrerbildung im Dezember 2014 mit der Gr{\"u}ndung des Zentrums f{\"u}r Lehrerbildung und Bildungsforschung (ZeLB). Aus der koordinierenden Arbeit des Zentrums entstand das fakult{\"a}ts{\"u}bergreifende Projekt „Professionalisierung - Schulpraktische Studien - Inklusion" (PSI-Potsdam) das im Rahmen der Qualit{\"a}tsoffensive Lehrerbildung des Bundesministeriums f{\"u}r Bildung und Forschung erfolgreich gef{\"o}rdert wurde (2015-2018) und dessen Verl{\"a}ngerung (2019-2023) bewilligt ist. Der vorliegende Band vermittelt in den drei großen Kapiteln „Erhebungsinstrumente", „Seminarkonzepte" und „Vernetzungen" einen {\"U}berblick {\"u}ber einige der praxisnahen Forschungszug{\"a}nge, hochschuldidaktischen Ans{\"a}tze und Strategien zur Vernetzung innerhalb der Lehrerbildung, die im Rahmen von PSI-Potsdam entwickelt und umgesetzt wurden. Die Beitr{\"a}ge wurden mit dem Ziel verfasst, Kolleginnen und Kollegen an Universit{\"a}ten und Hochschulen, Akteur_innen des Vorbereitungsdiensts sowie der Fort- und Weiterbildung von Lehrkr{\"a}ften m{\"o}glichst konkrete Einblicke zu gew{\"a}hren. Unter der Herausgeberschaft von Prof. Dr. Andreas Borowski (Fachdidaktik Physik), Prof. Dr. Antje Ehlert (Inklusionsp{\"a}dagogik mit dem F{\"o}rderschwerpunkt Lernen) und Prof. Dr. Helmut Prechtl (Fachdidaktik Biologie) vereinen sich Autor_innen mit breit gestreuter fachdidaktischer und bildungswissenschaftlicher Expertise.}, language = {de} } @article{GerlachGlueckKunze2023, author = {Gerlach, Moritz and Gl{\"u}ck, Jochen and Kunze, Markus}, title = {Stability of transition semigroups and applications to parabolic equations}, series = {Transactions of the American Mathematical Society}, volume = {376}, journal = {Transactions of the American Mathematical Society}, number = {1}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/8620}, pages = {153 -- 180}, year = {2023}, abstract = {This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.}, language = {en} } @article{GerlachGlueck2017, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {On a convergence theorem for semigroups of positive integral operators}, series = {Comptes Rendus Mathematique}, volume = {355}, journal = {Comptes Rendus Mathematique}, publisher = {Elsevier}, address = {Paris}, issn = {1631-073X}, doi = {10.1016/j.crma.2017.07.017}, pages = {973 -- 976}, year = {2017}, abstract = {We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.}, language = {en} } @article{Gerlach2018, author = {Gerlach, Moritz Reinhardt}, title = {Convergence of dynamics and the Perron-Frobenius operator}, series = {Israel Journal of Mathematics}, volume = {225}, journal = {Israel Journal of Mathematics}, number = {1}, publisher = {Hebrew univ magnes press}, address = {Jerusalem}, issn = {0021-2172}, doi = {10.1007/s11856-018-1671-7}, pages = {451 -- 463}, year = {2018}, abstract = {We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.}, language = {en} } @article{GerlachGlueck2019, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Convergence of positive operator semigroups}, series = {Transactions of the American Mathematical Society}, volume = {372}, journal = {Transactions of the American Mathematical Society}, number = {9}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/7836}, pages = {6603 -- 6627}, year = {2019}, abstract = {We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.}, language = {en} } @article{EdekoGerlachKuehner2019, author = {Edeko, Nikolai and Gerlach, Moritz Reinhardt and K{\"u}hner, Viktoria}, title = {Measure-preserving semiflows and one-parameter Koopman semigroups}, series = {Semigroup forum}, volume = {98}, journal = {Semigroup forum}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0037-1912}, doi = {10.1007/s00233-018-9960-3}, pages = {48 -- 63}, year = {2019}, abstract = {For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.}, language = {en} } @article{GerlachGlueck2018, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Lower bounds and the asymptotic behaviour of positive operator semigroups}, series = {Ergodic theory and dynamical systems}, volume = {38}, journal = {Ergodic theory and dynamical systems}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {0143-3857}, doi = {10.1017/etds.2017.9}, pages = {3012 -- 3041}, year = {2018}, abstract = {If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.}, language = {en} } @article{GerlachGlueck2019, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Mean ergodicity vs weak almost periodicity}, series = {Studia mathematica}, volume = {248}, journal = {Studia mathematica}, number = {1}, publisher = {Polska Akademia Nauk, Instytut Matematyczny}, address = {Warszawa}, issn = {0039-3223}, doi = {10.4064/sm170918-20-3}, pages = {45 -- 56}, year = {2019}, abstract = {We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .}, language = {en} }