Palle E. T. Jorgensen

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In this paper we show how wavelets originating from multireso-lution analysis of scale N give rise to certain representations of the Cuntz algebras O N , and conversely how the wavelets can be recovered from these representations. The representations are given on the Hilbert space L 2 (Ì) by (S i ξ) (z) = m i (z) ξ z N ¡. We characterize the Wold(More)
We identify sets of conjugacy classes of ergodic endomorphisms of B(H) where H is a xed separable Hilbert space. They correspond to certain equivalence classes of pure states on the Cuntz algebras O n where n is the Powers index. These states, called nitely correlated states, and strongly asymptotically shift invariant states, are deened and characterized.(More)
Let Od be the Cuntz algebra on generators S1, . . . , Sd, 2 ≤ d < ∞, and let Dd ⊆ Od be the abelian subalgebra generated by monomials SαS ∗ α = Sα1 · · ·SαkS ∗ αk · · ·S α1 where α = (α1 . . . αk) ranges over all multi-indices formed from {1, . . . , d}. In any representation of Od, Dd may be simultaneously diagonalized. Using S i (SαS ∗ α) = S iα S iα S i(More)
This thesis focuses on measuring extreme risks in insurance business. We mainly use extreme value theory to develop asymptotics for risk measures. We also study the characterization of upper comonotonicity for multiple extreme risks. Firstly, we conduct asymptotics for the Haezendonck–Goovaerts (HG) risk measure of extreme risks at high confidence levels,(More)
Anderson and Frazier [6] defined a generalization of factorization in integral domains called τ -factorization. If D is an integral domain and τ is a symmetric relation on the nonzero nonunits of D, then a τ -factorization of a nonzero nonunit a ∈ D is an expression a = λa1 · · · an, where λ is a unit in D, each ai is a nonzero nonunit in D, and aiτaj for i(More)
We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang–Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the bijective correspondence between based harmonic spheres in the(More)
In this paper, we first review one of difficult parts of the proof of Witten's conjecture by Kontsevich that had not been emphasized before. In the derivation of the KdV equations, we review the boson-fermion correspondence method [17] to show that the trajectory of GL∞ action on 1 as an element of the ring C[x 1 , x 2 , · · · ] yields the solutions of KP(More)
Let Od be the Cuntz algebra on generators S1, . . . , Sd, 2 ≤ d < ∞, and let Dd ⊆ Od be the abelian subalgebra generated by monomials SαS ∗ α = Sα1 · · ·SαkS ∗ αk · · ·S α1 where α = (α1 . . . αk) ranges over all multi-indices formed from {1, . . . , d}. In any representation of Od, Dd may be simultaneously diagonalized. Using S i (SαS ∗ α) = ( S iα S∗ iα )(More)