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Complete Nevanlinna-Pick kernels [article]

Jim Agler, John E. McCarthy
2016 arXiv   pre-print
We show that a kernel has the matrix-valued Nevanlinna-Pick property if and only if it has the vector-valued Nevanlinna-Pick property.  ...  We give a representation of all complete Nevanlinna-Pick kernels, and show that they are all restrictions of a universal complete Nevanlinna-Pick kernel.  ...  In particular, having the vector-valued Nevanlinna-Pick property is equivalent to having the complete Nevanlinna-Pick property.  ... 
arXiv:1610.01997v1 fatcat:it4jwvbt6bbozasvzzo2z4dgdi

Nevanlinna-Pick Kernels and Localization [article]

Jim Agler, John E. McCarthy
2016 arXiv   pre-print
We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in C^d for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly  ...  Introduction This paper concerns a generalization of the following result due to Pick [P] and Nevanlinna [N] .  ...  Our second application constitutes a generalization of the classical Nevanlinna-Pick interpolation theorem to the ball.  ... 
arXiv:1610.01965v1 fatcat:q5bkk57zrjab3hdpqxfomkroka

Pick Interpolation for free holomorphic functions [article]

Jim Agler, John E. McCarthy
2013 arXiv   pre-print
The Pick problem is to determine whether or not there is a function in H ∞ 1 (U) that maps each λ i to the corresponding w i .  ...  In Section 4, we give a description in Theorem 4.6 of all the solutions of a (solvable) Pick problem -this is called the Nevanlinna problem.  ... 
arXiv:1308.3730v1 fatcat:6tmozdut7jaonbjl3ulk2cxq7u

Weak products of complete Pick spaces [article]

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter
2020 arXiv   pre-print
The results hold for many weighted Besov spaces ℋ in the unit ball of ℂ^d provided the reproducing kernel has the complete Pick property.  ...  complete Pick kernel.  ...  An important example of such a complete Pick kernel is the Szegő kernel k w (z) = (1 − wz) −1 .  ... 
arXiv:1804.10693v2 fatcat:lcbkvekgnzhk3lpztsiqlumu2i

Picking the right PDA

John J. Fried
2006 Community Oncology  
Screens Don't be seduced just because a PDA's screen displays beautiful colors John Fried is the technology columnist for the Philadelphia Inquirer. and sharp text.  ... 
doi:10.1016/s1548-5315(11)70672-6 fatcat:hbgl5egv5fb7zo2rb5owxbqmzy

The three point Pick problem on the Bidisk [article]

Jim Agler, John E. McCarthy
2016 arXiv   pre-print
We analyze the three point Pick interpolation problem on the bidisk  ...  Pick in 1916 [9] , who showed that a necessary and sufficient condition is that the Pick matrix 1 −w i w j 1 −λ i λ j N i,j=1 be positive semi-definite.  ...  The two point Pick problem on the bidisk is easily analyzed.  ... 
arXiv:1610.02382v1 fatcat:lboktcyb6vemdfdozatnnmu4fe

Top Picks From Year 2020

Lizy Kurian John
2021 IEEE Micro  
Top Picks From Year 2020 Lizy Kurian John, The University of Texas at Austin, TX, 78712, USA W e have lived more than one year in the special circumstances created by .  ...  The purpose of the Top Picks issue has been multifold.  ... 
doi:10.1109/mm.2021.3074759 fatcat:7dx36e3vknebrecpmhwk3ynd3y

Spaces of Dirichlet series with the complete Pick property [article]

John E. McCarthy, Orr Shalit
2015 arXiv   pre-print
We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s,u) = ∑ a_n n^-s-u̅, and characterize when such a space is a complete Pick space.  ...  Thus, a family of multiplier algebras of Dirichlet series are exhibited with the property that every complete Pick algebra is a quotient of each member of this family.  ...  If H has the m-Pick property for all positive natural numbers, we say it has the complete Pick property.  ... 
arXiv:1507.04162v2 fatcat:hwgw2i2frzenbd2jmx5pb42zxu

An H^p scale for complete Pick spaces [article]

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter
2020 arXiv   pre-print
We define by interpolation a scale analogous to the Hardy H^p scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call ℋ^p.  ...  Let k be a normalized complete Pick kernel on X.  ...  Their proof carries over to any complete Pick space. We first prove the easy implication, which is valid without the complete Pick assumption.  ... 
arXiv:2005.08909v2 fatcat:2c4bm46iwrf35ipblvmk32644a

Free outer functions in complete Pick spaces [article]

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter
2022 arXiv   pre-print
They show that every function f in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type f=φ g, where g is cyclic, φ is a contractive multiplier, and  ...  It is a property of complete Pick kernels, that a Pick problem has a solution, if and only if the Pick matrix P ≥ 0, i.e. P a, a ≥ 0 for all a ∈ C n , see [41] , [51] , [40] ; see also [2] .  ...  A Pick problem is called extremal, if P ≥ 0 and rank P < rank K.  ... 
arXiv:2203.08179v1 fatcat:s7i7jfyiancoznzgz7fjyoakyi

On the isomorphism question for complete Pick multiplier algebras [article]

Matt Kerr, John E. McCarthy, Orr Shalit
2013 arXiv   pre-print
Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra = {f|_V : f ∈_d}, where d is some integer or ∞, _d is the multiplier algebra of the Drury-Arveson space  ...  By universality of H 2 d , every multiplier algebra of an irreducible complete Pick kernel is of the form M V for some d and some variety V ⊆ B d (see [1] ).  ... 
arXiv:1211.1116v2 fatcat:phcskb63ebchfmtguaqjlats3a

Interpolating sequences in spaces with the complete Pick property [article]

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter
2020 arXiv   pre-print
We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property.  ...  If k has the M n Pick property for every n, we say the kernel, and the corresponding Hilbert space H k , have the complete Pick property or the complete Nevanlinna-Pick property.  ...  When n = 1, we say k has the Pick property.  ... 
arXiv:1701.04885v2 fatcat:xrj4amwjvzbhdk22neiy3i6z4a

Better, faster, cheaper: Pick any three

Paul Clements, John McGregor
2012 Business Horizons  
The following papers have been pubished as part of that effort: //dx.doi.org/10.1016/j.bushor.2011.12.001. 2/12 Paul Clements and John D. McGregor. Better, faster, cheaper, pick any three.  ...  Papers or Reports 2012 Paul Clements and John McGregor. Better, faster, cheaper: Pick any three, http:Product Line. SPLC 2011: 277-286 8/11 Silvia Abrahão, Andy J. Nolan, Paul C.  ... 
doi:10.1016/j.bushor.2011.12.001 fatcat:m2vhmc4n4veplk4pbxx5gxndji

Polynomials and spatial Pick-type theorems

Krzysztof Kołodziejczyk, John Reay
2008 Expositiones mathematicae  
We also study some relationships between lattice points in a lattice polyhedron which lead to some new Pick-type formulae.  ...  Another purpose of this paper is to pose several problems related to the subject of higher-dimensional Pick-type theorems.  ...  Pick-type formulae involving fewer lattice points In this section we give formulae for the volume of lattice polyhedra which employ either fewer lattices or fewer lattice points than in the previously  ... 
doi:10.1016/j.exmath.2007.06.001 fatcat:imoh63er7rb7npfghpuhvc5xly

Radially weighted Besov spaces and the Pick property [article]

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter
2018 arXiv   pre-print
Furthermore we show that if a weight ω satisfies that for some α >-1 the ratio ω(z)/(1-|z|^2)^α is nondecreasing for t_0<|z|<1, then B^s_ω is a complete Pick space, whenever s> (α+d)/2.  ...  We will say that a Hilbert function space H is a complete Pick space, if there is an equivalent norm on the space such that the reproducing kernel for that norm is a normalized complete Pick kernel.  ...  Radial weights and complete Pick spaces Our result on radially weighted Besov spaces that are complete Pick spaces is based on the following Lemma. 1 1 − tz dµ(t) = 1 1 − ∞ n=1 c n z n for all |z| < 1  ... 
arXiv:1807.00730v1 fatcat:7mub6dlyarc3lnmcan7o6d7424
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