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pro vyhledávání: '"Dungen, P. van den"'
Autor:
Dungen, Koen van den
In this article we study generalised Dirac-Schr\"odinger operators in arbitrary signatures (with or without gradings), providing a general KK-theoretic framework for the study of index pairings and spectral flow. We provide a general Callias-type The
Externí odkaz:
http://arxiv.org/abs/2407.02993
Autor:
Dungen, Koen van den
We consider generalised Dirac--Schr\"odinger operators, consisting of a self-adjoint elliptic first-order differential operator D with a skew-adjoint 'potential' given by a (suitable) family of unbounded operators. The index of such an operator repre
Externí odkaz:
http://arxiv.org/abs/2312.17600
Publikováno v:
J. Math. Anal. Appl. 522 (1) (2023) 127002
We show by (counter)example that the intersection of complemented submodules in a Hilbert $C^*$-module is not necessarily complemented, answering an open question from [MR].
Comment: Addendum to : The Friedrichs angle and alternating projections
Comment: Addendum to : The Friedrichs angle and alternating projections
Externí odkaz:
http://arxiv.org/abs/2302.04631
Autor:
Dungen, Koen van den
Publikováno v:
International Mathematics Research Notices, Volume 2023, Issue 9, May 2023, Pages 7578-7615
In the context of the Kasparov product in unbounded KK-theory, a well-known theorem by Kucerovsky provides sufficient conditions for an unbounded Kasparov module to represent the (internal) Kasparov product of two other unbounded Kasparov modules. In
Externí odkaz:
http://arxiv.org/abs/2006.10616
Autor:
Dungen, Koen van den, Ronge, Lennart
Publikováno v:
Operators and Matrices 15 (2021), 1393-1416
We study the Atiyah-Patodi-Singer (APS) index, and its equality to the spectral flow, in an abstract, functional analytic setting. More precisely, we consider a (suitably continuous or differentiable) family of self-adjoint Fredholm operators $A(t)$
Externí odkaz:
http://arxiv.org/abs/2004.01085
Autor:
Dungen, Koen van den, Mesland, Bram
Publikováno v:
Ann. K-Th. 5 (2020) 501-537
We propose a new notion of unbounded $K\!K$-cycle, mildly generalising unbounded Kasparov modules, for which the direct sum is well-defined. To a pair $(A,B)$ of $\sigma$-unital $C^{*}$-algebras, we can then associate a semigroup $\overline{U\!K\!K}(
Externí odkaz:
http://arxiv.org/abs/1907.04049
Autor:
Dungen, Koen van den
Publikováno v:
Journal of Topology and Analysis 14 (2022), 147-181
We study the Kasparov product on (possibly non-compact and incomplete) Riemannian manifolds. Specifically, we show on a submersion of Riemannian manifolds that the tensor sum of a regular vertically elliptic operator on the total space and an ellipti
Externí odkaz:
http://arxiv.org/abs/1811.07824
Autor:
Dungen, Koen van den
Publikováno v:
Annales Henri Poincar\'e, 20 (2019), 3007-3017
We improve our previous results on indefinite Kasparov modules, which provide a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. In particular, we can weaken the assumptions that are i
Externí odkaz:
http://arxiv.org/abs/1807.11856
Autor:
Dungen, Koen van den
Publikováno v:
Journal of Mathematical Physics 59 (2018), 063507
We study a noncommutative analogue of a spacetime foliated by spacelike hypersurfaces, in both Riemannian and Lorentzian signatures. First, in the classical commutative case, we show that the canonical Dirac operator on the total spacetime can be rec
Externí odkaz:
http://arxiv.org/abs/1711.07299
Autor:
Dungen, Koen van den
Publikováno v:
Journal of Spectral Theory 9 (2019), 1459-1506
We study the relation between spectral flow and index theory within the framework of (unbounded) KK-theory. In particular, we consider a generalised notion of 'Dirac-Schr\"odinger operators', consisting of a self-adjoint elliptic first-order differen
Externí odkaz:
http://arxiv.org/abs/1710.09206