| 1. |
- Silvestrov, Sergei, et al.
(author)
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Topological dynamical systems of type I
- 2002
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In: Expositiones Mathematicae. - 0723-0869. ; 20:2, s. 117-142
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Journal article (peer-reviewed)abstract
- The equivalence of existence of a Borel section to nonexistence of recurrent aperiodic points for homeomorphisms of locally compact topological spaces is proved using the theory of C*-algebras.
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| 2. |
- Agranovsky, M., et al.
(author)
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Malmheden's theorem revisited
- 2010
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In: Expositiones mathematicae. - : Elsevier BV. - 0723-0869 .- 1878-0792. ; 28:4, s. 337-350
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Journal article (peer-reviewed)abstract
- In 1934 Malmheden [16] discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin (1957) [8] 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in R-n.
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| 3. |
- Carlsson, Marcus
(author)
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von Neumann's trace inequality for Hilbert–Schmidt operators
- 2021
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In: Expositiones Mathematicae. - : Elsevier BV. - 0723-0869. ; 39:1, s. 149-157
-
Journal article (peer-reviewed)abstract
- von Neumann's inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.
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| 4. |
- Gudmundsson, Sigmundur, et al.
(author)
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On the geometry of tangent bundles
- 2002
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In: Expositiones Mathematicae. - 0723-0869. ; 20:1, s. 1-41
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Journal article (peer-reviewed)
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| 5. |
- Hellstrom, L, et al.
(author)
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Two-sided ideals in q-deformed Heisenberg algebras
- 2005
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In: Expositiones Mathematicae. - : Elsevier BV. - 0723-0869. ; 23:2, s. 99-99
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Journal article (peer-reviewed)abstract
- In this article, the structure of two-sided ideals in the q-deformed Heisenberg algebras defined by the q-deformed Heisenberg canonical commutation relation AB-qBA=I is investigated. We show that these algebras are simple if and only if q = 1. For q not equal 1, 0 we present an infinite descending chain of non-trivial two-sided ideals, thus deducing by explicit construction that the q-deformed Heisenberg algebras are not just non-simple but also non-artinian for q not equal 1, 0. We establish a connection between the quotients of the q-deformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in q-deformed Heisenberg algebras, investigate properties of deformed commutator mappings, show their fundamental importance for investigation of ideals in q-deformed Heisenberg algebras, and demonstrate how to apply these results to the investigation of faithfulness of representations of q-deformed Heisenberg algebras.
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| 6. |
- Konstantopoulos, Takis, et al.
(author)
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A fully stochastic approach to limit theorems for iterates of Bernstein operators
- 2018
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In: Expositiones mathematicae. - : Elsevier BV. - 0723-0869 .- 1878-0792. ; 36:2, s. 143-165
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Journal article (peer-reviewed)abstract
- This paper presents a stochastic approach to theorems concerning the behavior of iterations of the Bernstein operator B-n taking a continuous function f is an element of C[0, 1] to a degree-n polynomial when the number of iterations k tends to infinity and n is kept fixed or when n tends to infinity as well. In the first instance, the underlying stochastic process is the so-called Wright-Fisher model, whereas, in the second instance, the underlying stochastic process is the Wright-Fisher diffusion. Both processes are probably the most basic ones in mathematical genetics. By using Markov chain theory and stochastic compositions, we explain probabilistically a theorem due to Kelisky and Rivlin, and by using stochastic calculus we compute a formula for the application of B-n a number of times k = k(n) to a polynomial f when k(n)/n tends to a constant.
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| 7. |
- Silvestrov, Sergei, et al.
(author)
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C*-crossed products and shift spaces
- 2007
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In: Expositiones Mathematicae. - : Elsevier BV. - 0723-0869. ; 25:4, s. 275-307
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Journal article (peer-reviewed)abstract
- We use Exel's C*-crossed products associated to non-invertible dynamical systems to associate a C*-algebra to arbitrary shift space. We show that this C*-algebra is canonically isomorphic to the C*-algebra associated to a shift space given by Carlsen [Cuntz–Pimsner C*-algebras associated with subshifts, Internat. J. Math. (2004) 28, to appear, available at arXiv:math.OA/0505503], has the C*-algebra defined by Carlsen and Matsumoto [Some remarks on the C*-algebras associated with subshifts, Math. Scand. 95 (1) (2004) 145–160] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space. We also consider its representations and its relationship to other C*-algebras associated to shift spaces. We show that it can be viewed as a generalization of the universal Cuntz–Krieger algebra, discuss uniqueness and present a faithful representation, show that it is nuclear and satisfies the Universal Coefficient Theorem, provide conditions for it being simple and purely infinite, show that the constructed C*-algebras and thus their K-theory, K0 and K1, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and present a description of the structure of gauge invariant ideals.
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