Palle Jorgensen
University of Iowa, Mathematics, Faculty Member
- Highest Degree, PhD Mathematics, 1973, Aarhus University, Denmark. Also from Aarhus University, MS 1970, and BA 1968.... moreHighest Degree, PhD Mathematics, 1973, Aarhus University, Denmark. Also from Aarhus University, MS 1970, and BA 1968.
Professional and Academic Positions, reverse chronology:
1983-Present: Professor, Department of Mathematics, University of Iowa
1982-84: Visiting Associate Professor, Department of Mathematics, University of Pennsylvania (on leave from Aarhus first year, and from Iowa second year; NSF grant, R.V. Kadison, PI).
1980-82: Associate Professor, Mathematics Institute, Aarhus University, Denmark, on leave from Stanford the first year (Danish Research Council grants).
1977-80: Assistant Professor, Department of Mathematics, Stanford University.
1973-77: Postdoctoral Research Fellow, University of Pennsylvania, support from the Danish Natural Science Research Council; partial support from the NSF, Grant MCS 77-02831, 1977, under R.V. Kadison, PI).
A selection of 5 recent publications by Jorgensen. From the AMS MathSciNet list: authors (alphabetic), title, journal title (abbreviated), vol, year, and page numbers:
Jorgensen, Palle E. T.; Pearse, Erin P. J. Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces. J. Math. Anal. Appl. 469 (2019), no. 2, 765–807.
Jorgensen, Palle E. T.; Song, Myung-Sin. Markov chains and generalized wavelet multiresolutions. J. Anal. 26 (2018), no. 2, 259–283.
Jorgensen, Palle; Tian, Feng. Infinite weighted graphs with bounded resistance metric. Math. Scand. 123 (2018), no. 1, 5–38.
Jorgensen, Palle E. T. 10 lectures CBMS; Harmonic analysis: Smooth and non-smooth. Published for the Conference Board of the Mathematical Sciences. CBMS Regional Conference Series in Mathematics, 128. American Mathematical Society, Providence, RI, 2018. xi+266 pp. ISBN: 978-1-4704-4880-6.
Jorgensen, P. E.; Shah, Firdous A.; Ahmad, O.; Fractional wave packet systems in L2(R).
J. Math. Phys. 59(2018), no. 7, 073509, 20 pp.edit
Research Interests:
In the present paper, we consider the marginal entropy of the a pure state in the tensor product of two Hilbert spaces. The expectation of the marginal entropy of a random pure state with respect to the Haar measure of unitary... more
In the present paper, we consider the marginal entropy of the a pure state in the tensor product of two Hilbert spaces. The expectation of the marginal entropy of a random pure state with respect to the Haar measure of unitary transformation on the tensor product Hilbert space depends on group integrals of unitary group. For group integrals of ordinary representation matrix elements of $\rm U(n)$, we provide a elementary method to reobtain Weingarton's result of asymptotical behavior of group integrals. For group integrals of matrix elements of irreducible representations of $\rm U(n)$,we generalize the Weyl-Schur duality theorem and get an algorithm.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Let [Formula: see text]. Given a closed set [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the set of tuples of nonnegative integers [Formula: see text] with [Formula: see text] for finitely many [Formula:... more
Let [Formula: see text]. Given a closed set [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the set of tuples of nonnegative integers [Formula: see text] with [Formula: see text] for finitely many [Formula: see text], the [Formula: see text]-moment problem on [Formula: see text] entails determining whether or not there exists a measure [Formula: see text] on [Formula: see text] so that [Formula: see text] and [Formula: see text] We prove that [Formula: see text] exists if and only if a natural analogue of the Riesz–Haviland functional [Formula: see text] is [Formula: see text]-positive, i.e. if [Formula: see text] is any polynomial which is nonnegative for all [Formula: see text], then [Formula: see text] We will also provide a sufficient condition for [Formula: see text] to be unique, an analogue of a celebrated theorem of K. Schmüdgen and an application to stochastic processes.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests: Mathematics and Sigma
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise... more
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise linking between such two Hilbert spaces when it is assumed that D is dense in one of the two; but generally not in the other. No relative boundedness is assumed. Nonetheless, under natural assumptions (motivated by potential theory), we prove a theorem where a comparison between the two Hilbert spaces is made via a specific selfadjoint semibounded operator. Applications include physical Hamiltonians, both continuous and discrete (infinite network models), and operator theory of reflection positivity.
Research Interests:
In this paper we study the Foias-Williams operator T ( H g ) = ( S ∗ a m p ; H g 0 a m p ; S ) \begin{equation*}T(H_{g})=\begin {pmatrix}S^{*} & H_{g} \ 0 & S \end{pmatrix} \end{equation*} where g ∈ L ∞ g\in L^{\infty } , and H g H_{g}... more
In this paper we study the Foias-Williams operator T ( H g ) = ( S ∗ a m p ; H g 0 a m p ; S ) \begin{equation*}T(H_{g})=\begin {pmatrix}S^{*} & H_{g} \ 0 & S \end{pmatrix} \end{equation*} where g ∈ L ∞ g\in L^{\infty } , and H g H_{g} is a Hankel operator with symbol g g . We exhibit a relationship between the similarity of T ( H g ) T(H_{g}) to a contraction and the rate of decay of { | g n | } n = 0 ∞ \{|g_{n}|\}_{n=0}^{\infty } , the absolute values of the Fourier coefficients of the symbol g g .
Research Interests:
This paper is concerned with a class of complete second order linear differential equations in a Banach space. We show the existence and uniqueness of classical solutions of (SE) { u ( t ) = A ( t ) u ′ ( t ) + B ( t ) u ( t ) + f ( t )... more
This paper is concerned with a class of complete second order linear differential equations in a Banach space. We show the existence and uniqueness of classical solutions of (SE) { u ( t ) = A ( t ) u ′ ( t ) + B ( t ) u ( t ) + f ( t ) for t ∈ [ 0 , T ] u ( 0 ) = x and u ′ ( 0 ) = y . \begin{equation}\tag {SE} \begin {cases} u(t) = A(t)u’(t) + B(t)u(t) + f(t) \text {for $t \in [0,T]$} \ u(0) = x \text {and} u’(0) = y. \end{cases} \end{equation}
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD),... more
Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and ...
Research Interests:
To evaluate the thromboprophylactic use of low molecular weight heparins (LMWHs), publications from 27 orthopaedic trials and 35 studies of patients undergoing general or gynaecological surgery were scrutinized and subjected to a partial... more
To evaluate the thromboprophylactic use of low molecular weight heparins (LMWHs), publications from 27 orthopaedic trials and 35 studies of patients undergoing general or gynaecological surgery were scrutinized and subjected to a partial meta-analysis. In orthopaedic surgery, LMWHs were superior to placebo or dextran and at least as efficient as unfractionated heparin in the prevention of deep vein thrombosis (DVT). Compared with unfractionated heparin, one of the LMWH preparations signficantly reduced the total incidence of DVT. The rate of non-fatal pulmonary embolism was 0.49 per cent in patients receiving LMWH and 1.22 per cent in controls. Seven orthopaedic patients (0.15 per cent) died from pulmonary embolism, none of whom received LMWH. In general surgery, the LMWHs were at least as efficient as unfractionated heparin, with a trend towards a lower risk of pulmonary embolism with the former. Compared with unfractionated heparin, LMWHs did not reduce the postoperative mortality...
Research Interests:
Localized bases in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mm
Research Interests:
Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the... more
Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the Hilbert space of square-integrable functions on the unit-interval, both with respect to Lebesgue measure, and also with respect to a wider class of self-similar measures (mu). That is, we consider recursive and orthogonal decompositions for the Hilbert space L^2(mu) where mu is some self-similar measure on [0,1]. Up to two specific reflection symmetries, our scheme produces infinite families of orthonormal bases in L^2(0,1). Our approach is as versatile as the more traditional spline constructions. But while singly generated spline bases typically do not produce orthonormal bases, each of our present algorithms does.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
In this chapter, we collect definitions and some basic facts about the underlying spaces, endomorphisms, measurable partitions, etc., which are used throughout the book. Though these notions are known in ergodic theory, we discuss them... more
In this chapter, we collect definitions and some basic facts about the underlying spaces, endomorphisms, measurable partitions, etc., which are used throughout the book. Though these notions are known in ergodic theory, we discuss them for the reader’s convenience.
