
	Where results make sense

Topic: Polydisk

	ST Product News: Gato, Polydisk, Mi-Print
		The Polydisk is a 4 by 6-1/2 by 1-1/2 inch grey box that plugs into the cartridge slot of your 520 or 1040 ST To create the RAMdisk, simply use the setup program included with Polydisk to decide how much of the Polydisk's 512K memory you want to use.
		The Polydisk initialization program then sits in the Auto folder of your boot disk, so every time you turn on your ST the RAMdisk is instantly accessable.
		Since the Polydisk is an external peripheral, a warm boot (pressing the reset button on the back of the computer without turning off the power) won't erase the files you've stored in the Polydisk.
	www.atarimagazines.com /v6n9/STProductReviews.html (1561 words)

	sem11_1
		Following the work of Agler on the Nevanlinna--Pick interpolation for the polydisk, Ball--Trent and Kalyuzhniy-Verbovetsky have studied $d$-dimensional conservative discrete-time i/s/o systems of Roesser and Fornasini-Marchesini type respectively and their transfer functions.
		In the case of $d=2$ it is possible to construct explicitly two extremal decompositions of the scattering subspace so that any decomposition is contained (in a certain sense) between these two.
		Unlike in the one-dimensional case, the definition of the incoming, the outgoing, and the scattering subspaces for a scattering system with $d$ evolution operators depends on the choice of the ``cut'' between the past and the future, i.e., on the choice of the future cone.
	arts-sciences.cua.edu /math/MIO/sem11_1.htm (468 words)

	Conference Program Online
		Function theory on the unit disk, specifically the study of Hardy spaces (of vector- or operator-valued analytic functions) on the unit disk, has been a standard tool in the frequency domain approach to a number of problems in system and control theory and in signal processing.
		Until recently, advances on multivariable generalizations of these ideas (where the unit disk is replaced by the polydisk and analytic functions of a single variable are replaced by analytic functions of several variables) have been rather piecemeal and sporadic.
		The purpose of this MInisymposium is to draw attention to a number of new developments in multivariable function theory which also have impact in engineering.
	meetings.siam.org /sess/dsp_programsess.cfm?SESSIONCODE=768 (210 words)

	Citebase - A Schwarz lemma on the polydisk (Site not responding. Last check: 2007-10-14)
		Authors: Knese, Greg E. There is a known generalization of the classical Schwarz lemma to holomorphic functions from the polydisk to the disk.
		In this paper, we characterize those functions which satisfy equality everywhere in this generalized inequality: they are the transfer function of an n+1 by n+1 symmetric unitary, and in particular, are rational, inner, and belong to the Schur-Agler class of the polydisk.
		We also present some sufficient conditions for a function to be of this type.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0512452 (198 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		We present a generalization of these ideas for contractive analytic functions on the polydisk, multidimensional input/state/output systems, and scattering systems with several evolution operators.
		It turns out that while any contractive analytic function on the polydisk can be realized as the scattering function of an essentially unique scattering system, the relationship between scattering systems and input/state/output systems is considerably more complicated in the multidimensional case.
		We give a complete analysis for the case of dimension 2, recovering von Neumann inequality for pairs of commuting contractions, and discuss the outstanding issues in the higher dimensional case.
	www.math.technion.ac.il /~techm/20020319161020020319vin (211 words)

	Atlas: On the action of Toeplitz Operators in the unit polydisk. by Romi Shamoyan (Site not responding. Last check: 2007-10-14)
		Atlas: On the action of Toeplitz Operators in the unit polydisk.
		In recent decades numerouse papers were devoted to the study of the action of Th Toeplitz operators in different spaces of holomorphic functions in the unit polydisk and unit ball.
		The aim of the announcement is to provide new criteria for boundedness of Th operators in polydisk (with additional assumptions on X) The proof of the theorem is based on estimates for Tent spaces from (2)
	atlas-conferences.com /cgi-bin/abstract/catf-16 (217 words)

	Institute of Mathematics of National Academy of Sciences of Armenia (Site not responding. Last check: 2007-10-14)
		Harutjunian, A characteristic of unisotropic spaces of functions holomorphic in the polydisk, pp.
		The paper presents a complete characterization of those $h\in L^1(T^n)$ for which the Toeplitz operator $T_h(f)$ is a bounded operator acting in some weighted spaces $H^p(\a)$ of functions $f$ analytic in the unit polydisk $U^n$ of $C^n$ having the distinguished boundary $T^n$.
		Since seventies weighted $\overline{\partial}$-integral representations of smooth functions play an important part in multidimensional complex analysis and have numerous applications.
	math.sci.am /Journal/1995_2.html (485 words)

	Turcu's talk (Site not responding. Last check: 2007-10-14)
		The talk concerns an extension of the notion of Schur coefficients to the framework of w*-continuous Schur class maps.
		The particular case of special interest is the slice map associated to a several variable analytic function in the closed unit ball of $H^\infty$ of the unit polydisk.
		The resulting objects extend the classical Schur coefficients and can be used for instance to describe rational inner functions in the polydisk algebra.
	www.math.bgu.ac.il /~vinnikov/otseminar/abstracts/Turcu_11December2006/index.html (80 words)

	Gurevich's talk (Site not responding. Last check: 2007-10-14)
		Due to Lubin and Tate, it is a h-1 dimensional polydisk and any choice of a universal deformation of F fixes a parametrisation on it.
		We also have a natural action of the automorphism group of F on the polydisk.
		This formula in particular allows to estimate the action of the natural filtration of the automorphism group of F on the Lubin-Tate polydisk.
	www.math.bgu.ac.il /~bessera/seminar/10March04 (182 words)

	Citebase - Composition operators on generalized Bloch spaces of the polydisk (Site not responding. Last check: 2007-10-14)
		We extend to the n-polydisk previous one-variable characterization results of K. Madigan on the p-Lipschitz space and K. Madigan/A. Matheson on the Bloch space by obtaining function-theoretic conditions on a holomorphic self-map of the polydisk such that the induced composition operator is bounded or compact between p- and q-Bloch spaces of the polydisk.
		These conditions turn out to be different in the cases when p is in (0,1) and when p is at least 1.
		Bounded composition operators on holomorphic Lipschitz spaces of the polydisk, preprint, 2002.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0507339 (409 words)

	Research
		Composition operators on generalized Bloch spaces of the polydisk, (with S. Stevic and Z. Zhou) submitted, 2005.
		Bounded composition operators on Lipschitz and Bloch spaces of the polydisk, to appear in
		Compact composition operators on boundary-regular, automorphism-invariant small spaces of the polydisk, in progress.
	staffwww.fullcoll.edu /dclahane/papers/papers.htm (188 words)

	Weekly Events 031003
		Boundedness and compactness of composition operators on holomorphic Lipschitz and Bloch spaces of the polydisk * Abstract
		We obtain a purely function-theoretic condition on p that completely characterizes the bounded composition operators on holomorphic Lipschitz and Bloch spaces of the polydisk.
		The definition of the geometrical mass is inspired by the role played by the Green's function for the conformal Laplacian and the Positive Mass Theorem in the solution to the Yamabe Problem.
	www.math.uci.edu /w11.html (348 words)

	Three Papers of Greg Knese (Site not responding. Last check: 2007-10-14)
		This paper concerns a generalization of the infinitesimal portion of the classical Schwarz lemma inequality to the setting of the polydisk.
		Specifically, we give a complete description of the functions that are extremal for this inequality at every point of the polydisk: they are the transfer function of a symmetric unitary.
		In addition, some sufficient conditions are given for a function to be of this type.
	www.math.wustl.edu /~geknese/paper.html (312 words)

	On The Bitangential Interpolation Problem For Contractive Valued Functions In The Polydisk - Alpay, Ball, Bolotnikov ...
		On The Bitangential Interpolation Problem For Contractive Valued Functions In The Polydisk (2000)
		This document uses CoBlitz to cache paper downloads.
		Alpay, J.A. Ball, and V. Bolotnikov, On the bitangential interpolation problem for contractive valued functions in the polydisk, J.Operator Theory, 44, 2000, 277--301.
	citeseer.ist.psu.edu /alpay00bitangential.html (433 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		As a consequence, the $H^{\infty}$-control problem for such a system becomes a Nevanlinna-Pick interpolation problem for Schur-class functions on the polydisk ${\mathbb D}^{d}$; interpolation nodes may be isolated points, or whole subvarieties of dimension $r$ less than $d$.
		The original result of Agler for interpolation on the polydisk leads to a sufficient (also necessary if $d=2$) condition for a solution in terms of existence of a solution to a certain Linear Matrix Inequality (LMI) rather than positivity of a single Pick matrix as in the classical $d=1$ case.
		For the case of interpolation along a variety of dimension $r \ge 1$, we arrive at an infinite LMI; how best to solve such an infinite LMI is a topic which remains to be explored.
	www.math.technion.ac.il /~techm/20020520141020020520bal (204 words)

	FactoryNetwork - Industrial Equipment - Item Details
		Polydisk 9 Disc Saveall, w/20HP motor & gearbox
		Item History Info: Plant closure - motivated to sell.
		Polydisk 9 Disc Saveall, w/20HP 1755RPM 460VAC motor, & Gearbox.
	www.factorynetwork.com /ItemDetail2.asp?ItemID=190 (123 words)

	Atlas: Products of Toeplitz operators on the Bergman space of the polydisk by Young Joo Lee (Site not responding. Last check: 2007-10-14)
		First, we extend the results to the polydisk.
		As a consequence on higher dimensional polydisks, we show that the generalized zero and compact product properties are the same for Toeplitz operators in a ceratin case.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # capg-99.
	atlas-conferences.com /cgi-bin/abstract/capg-99 (176 words)

	Recent Papers by Kehe Zhu (Site not responding. Last check: 2007-10-14)
		Compact Hankel operators on the Hardy space of the polydisk
		Composition operators induced by symbols defined on a polydisk, with Michael Stessin.
		Theory of Bergman Spaces in the Unit Ball, with Ruhan Zhao.
	math.albany.edu:8000 /~kzhu/papers.html (140 words)

	Analytic Hilbert Modules:1584883995:Chen, Xiaoman:eCampus.com
		Unitary equivalence of Hardy submodules on the unit polydisk
		Similarity of Hardy submodules on the unit polydisk
		Equivalence of Hardy submodules on the unit ball
	www.ecampus.com /bk_detail.asp?isbn=1584883995&referrer=yah04 (85 words)

	Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball
		We prove that these spaces are additionally norm-equivalent, thus extending known results for n=1 and the polydisk.
		Clahane, S. Stević, and Z. Zhou, “Composition operators on general Bloch spaces of the polydisk,” preprint, 2004, http://arxiv.org/abs/math.CV/0506424.
		Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Florida, 1995.
	www.hindawi.com /GetArticle.aspx?doi=10.1155/JIA/2006/61018&e=ref (428 words)

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