Michael Schwarz

ehemaliger Mitarbeiter

Kontakt
Raum:
2.09.2.15
Telefon:
+49 331 977-2748
...

Research interests & Preprints

Preprints

Research interests

  • Dirichlet forms
  • Dirichlet forms on graphs

 

Master's thesis

Boundary Representation of Dirichlet Forms on Discrete Spaces
Friedrich-Schiller Universität Jena, 2015

 

Publications

2020 | Courant's Nodal Domain Theorem for Positivity Preserving Forms | Matthias Keller, Michael SchwarzZeitschrift: Journal of Spectral TheorySeiten: 271–309Band: 10Link zur Publikation , Link zum Preprint

Courant's Nodal Domain Theorem for Positivity Preserving Forms

Autoren: Matthias Keller, Michael Schwarz (2020)

We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.

Zeitschrift:
Journal of Spectral Theory
Seiten:
271–309
Band:
10

2019 | Boundary representation of Dirichlet forms on discrete spaces | Matthias Keller, Daniel Lenz, Marcel Schmidt, Michael SchwarzZeitschrift: Journal de Mathématique Pure et AppliquéeSeiten: 109-143Band: 126Link zur Publikation , Link zum Preprint

Boundary representation of Dirichlet forms on discrete spaces

Autoren: Matthias Keller, Daniel Lenz, Marcel Schmidt, Michael Schwarz (2019)

We describe the set of all Dirichlet forms associated to a given infinitegraphin terms of Dirichlet forms on its Royden boundary. Our approach is purely analyticaland uses form methods.

Zeitschrift:
Journal de Mathématique Pure et Appliquée
Seiten:
109-143
Band:
126

2018 | The Kazdan-Warner equation on canonically compactifiable graphs | Keller, Matthias; Schwarz, MichaelZeitschrift: Calc. Var. Partial Differential EquationsSeiten: 18 pp.Band: 57Link zur Publikation , Link zum Preprint ,

The Kazdan-Warner equation on canonically compactifiable graphs

Autoren: Keller, Matthias; Schwarz, Michael (2018)

We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds.

Zeitschrift:
Calc. Var. Partial Differential Equations
Seiten:
18 pp.
Band:
57

Talks

  • Oberseminar Diskrete Spektraltheorie, Universität Potsdam. Talk: “Neumann problems on graphs.”
  • Oberseminar Geometric Analysis Seminar, Universität Bielefeld. Talk: “Courant’s nodal
    domain theorem for regular Dirichlet forms.”
  • Workshop Discrete and continuous models in the theory of networks, Zif Bielefeld. Poster:
     “Canonically compactifiable graphs.”
  • PhD Seminar, FSU Jena. Talk: “Courant’s nodal domain theorem on graphs.”
  • Oberseminar Diskrete Spektraltheorie Universität Potsdam. Talk: “Courant’s nodal do-
    main theorem for regular Dirichlet forms.”
  • Workshop Operator Theory and Indefinite Inner Product Spaces, TU Wien. Talk: “Bound-
    ary Representation of Dirichlet Forms on Canonically Compactifiable Graphs.”
  • Studierendenkonferenz der DMV, TU Berlin. Talk: “Randdarstellung von Dirichletfor-
    men auf Graphen.”
  • Workshop on Spectral Geometry, Universität Potsdam. Talk: “Boundary representation
    of Dirichlet forms on discrete spaces.”
  • Oberseminar Diskrete Spektraltheorie Universität Potsdam. Talk: “Dirichlet Forms on
    Canonically Compactifiable Graphs.”
  • One Day Workshop New directions in Mathematical Physics and beyond, FSU Jena. Talk:
    “Dirichlet forms on canonically compactifiable graphs.”