![[BGU Logo]](bgu_logo_small.gif)
Paul A. Fuhrmann
Welcome
to my homepage; It is still under construction, so please excuse the mess.
Under Construction
· comments may be
addressed to fuhrmannbgu@gmail.com
Address:
Department of Mathematics,
Ben-Gurion University of the Negev,
POB 653. Beer-Sheva 84105,
Israel.
- Office Telephone: 972-8-6461616
- Home Telephone: 972-8-6469262
- e-mail: fuhrmannbgu@gmail.com
- FAX: 972-8-6469343
Present
position:
Professor at the Department of Mathematics, Ben-GurionUniversity of the Negev
Research Interests:
My current research interests are in the following directions:
Algebraic System Theory, Behaviors, Observer Theory, Functional Models.
Announcement:
In June 1996 my book: A Polynomial Approach to Linear Algebra was
publishedby Springer.
A short announcementis enclosed. So are aEuropeanorder formas well as an
American order form.
- You can find a collection of photos, including many
members of the systemtheory community at the end of the home page.
- Any comments, suggestions for improvements are
encouraged and welcome.
Publications
LECTURE
NOTES:
LINEAR ALGEBRA
Books:
[1] P.A. Fuhrmann, Linear Operators and Systems in Hilbert
Space, McGraw-Hill, New York 1981.
[2] P.A. Fuhrmann, Editor, Proceedings of International
Symposium on the Mathematical Theory of Networks and Systems, MTNS-83,Springer,
Berlin 1984.
[3] R.W. Brockett and P.A. Fuhrmann eds. Special issue on "Linear
Control Theory", Linear Algebra and its Applications, April 1983.
[4] P.A. Fuhrmann, H. Kimura and J.C. Willems eds. Special issue on "Linear
Control Theory", Linear Algebra and its Applications, vols. 122-124, 1989.
[5] A.C. Antoulas, P. A. Fuhrmann, M.L.J. Hautus and Y. Yamamoto eds.
Special issue on "Linear Systems", Linear Algebra and its
Applications, 1993.
[6] P.A. Fuhrmann, A Polynomial Approach to Linear Algebra,
Springer Verlag, New York, 1996.
Its table of contents and preface are reproduced here.
Journals:
[76] P.A. Fuhrmann, "Observer theory", submitted, {\em
Lin. Alg. Appl.}.
[75] P.A. Fuhrmann and U. Helmke, "Tensored
polynomial models", to appear in the Giorgio Picci Festschrift.
[74] P.A. Fuhrmann, P. Rapisarda and Y.
Yamamoto, "On the state of behaviors", to appear, {\em Lin. Alg.
Appl.}.
[73] P.A. Fuhrmann, "On duality
in some problems of geometric control", {\em Acta Applicandae
Mathematicae}, (2006), 91, 207-251.
[72] P.A. Fuhrmann and J. Trumpf,
"On observability subspaces", {\em Int. J. Contr.}, (2006), 79,
1157-1195.
[71] P.A. Fuhrmann, "Autonomous subbehaviors and
output nulling subspaces", {\em Int. J. Contr.}, (2005), 78, 1378-1411.
[70] P.A. Fuhrmann, "A note on
continuous behavior homomorphisms", {\em Systems and Control Letters},
(2003), 49, 359-363.
[69] J. Trumpf, U. Helmke and P.A. Fuhrmann, "Towards
a compactification of the set of conditioned invariant subspaces", {\em
Systems and Control Letters.}, (2003), 48, 101-111.
[68] A. Gombani and P.A. Fuhrmann, "On a
connection between spectral factorization and geometric control theory",
{\em Int. J. Contr.}, (2002), 75, 824-859.
[67] P.A. Fuhrmann, "A study of
behaviors", {\em Lin. Alg. Appl.}, (2002), vols. 351-352, 303-380.
[66] P.A. Fuhrmann, "On
behavior homomorphisms and system equivalence", {\em Systems and Control
Letters.}, (2001), 44, 127-134.
[65] P.A. Fuhrmann and U. Helmke, "On
the parametrization of conditioned invariant subspaces and observer
theory", {\em Lin. Alg. Appl.}, (2001), vols. 332-334, 265-353.
[64] U. Helmke and P.A. Fuhrmann, "On
controllability of matrix eigenvalue algorithms: the inverse power
method", {\em Systems and Control Letters.}, (2000), 41, 57-66.
[63] P.A. Fuhrmann and A. Gombani, "On the
Lyapunov equation, coinvariant subspaces and partial ordering of inner
functions", {\em Int. J. Contr.}, (2000), vol. 73, 1129-1159.
[62] P.A. Fuhrmann and U. Helmke, "On the
parametrization of conditioned invariant subspaces", {\em Advances in
Mathematical Systems Theory}, Workshop in honour of D. Hinrichsen's 60th
birthday, April 20-23, 1999, Borkum Island.
[61] P.A. Fuhrmann, "On canonical Wiener-Hopf
factorizations", in {\em Dynamical Systems, Control, Coding, Computer
Vision}, G. Picci and D.S. Gilliam Eds., (1999), 69-91, Birkh\"auser
Verlag, Basel.
[60] P.A. Fuhrmann and A. Gombani, On a
Hardy space approach to the analysis of spectral factors, Int. J. Contr.,
(1998), vol.71, 277-357.
[59] P.A. Fuhrmann and U. Helmke,
Homeomorphisms between observable pairs and conditioned invariant subspaces,
Sys. and Contr. Letts., (1997), vol. 30, 217-223.
[58] U. Helmke and P.A. Fuhrmann, Tangent spaces
of rational functions, Lin. Alg. Appl., (1998), vol. 271, 1-40.
[57] U. Helmke and P.A. Fuhrmann, On complex
parametrizations of real rational functions, Arch. fur Elektr. und
Ubertragunstechnik, Special issue in memory of Wilhelm Cauer, (1995), vol. 49,
293-306.
[56] J. Hoffmann and P.A. Fuhrmann,
Factorization theory for stable inner, Journal of Mathematical Systems,
Estimation and Control, (1997), 7, 383-400.
[55] J. Hoffmann and P.A. Fuhrmann, On
balanced realizations for the classes of positive real and bounded real
transfer functions, Lin.Alg. Appl., (1996), 245, 107-146.
[54] P.A. Fuhrmann, On the characterization and
parametrization of minimal spectral factors, Journal of Mathematical Systems,
Estimation and Control, (1995), 5, 383-444.
[53] P.A. Fuhrmann, On skew primeness of inner
functions,Lin. Alg. Appl., (1994), vols. 208-209, 539-551.
[52] P.A. Fuhrmann, The bounded real characteristic
function and Nehari extensions, Operator Theory: Advances and Applications,
vol. 73, 264-315, Birkhauser Verlag, 1994.
[51] P.A. Fuhrmann, A duality theory for
robust control and model reduction, Lin. Alg. Appl., (1994), vols. 203-204,
471-578.
[50] R. Ober and P.A. Fuhrmann, Diffeomorphisms,
Proceeding of IMA workshop on "Applied Linear Algebra".
[49] P.A. Fuhrmann and R. Ober, On coprime
factorizations,the T. Ando Anniversary Volume, in Operator Theory: Advances and
Applications,vol. 62, 39-75. Birkhauser Verlag, 1993.
[48] J. Hoffmann and P.A. Fuhrmann,
Remarks on orthogonal polynomials and balanced realizations, Lin. Alg. Appl.,
(1994), vols. 205-206, 741-776.
[47] P.A. Fuhrmann, An algebraic approach to Hankel norm
approximation problems, L. Markus Festschrift, Lecture Notes in Pureand Applied
Mathematics, M. Dekker.
[46] J.C. Willems and P.A. Fuhrmann,
Stability theory for high order systems, Lin. Alg. Appl., (1992), 167, 131-149.
[45] P.A. Fuhrmann, Functional models in
linear algebra and its applications, Lin. Alg. Appl., (1992), vols. 162-164,
107-151.
[44] P.A. Fuhrmann and R. Ober, A functional
approach to LQG balancing, model reduction and robust control, Int. J. Contr.,
(1993),57, 627-741.
[43] P.A. Fuhrmann, Algebraic methods in system theory,
R.E. Kalman Festschrift, Springer Verlag, Berlin 1993, 233-265.
[42] P.A. Fuhrmann, A polynomial approach to
Hankel norm and balanced approximations, Lin. Alg. Appl., (1991), Vol. 146,
133-220.
[41] P.A. Fuhrmann, On the Hamiltonian structure in the
computation of singular values for a class of Hankel operators, in E. Mosca, L.
Pandolfi (eds.), $H^\infty$ Control Theory, Como, 1990;Lecture Notes in
Mathematics Vol. 1496, 250-276. Springer Verlag, Berlin1991.
[40] P.A. Fuhrmann, Elements of Factorization Theory,in H.
Nijmeijer, J.M.S. Schumacher (eds.). Three Decades of Mathematical System
Theory. A Collection of Surveys at the Occasion of the Fiftieth Birthday of Jan
C. Willems. Lecture Notes in Control and Information Sciences Vol. 135.
Springer Verlag, Berlin 1989.
[39] P.A. Fuhrmann and B.N. Datta, On
Bezoutians,Van der Monde matrices and the Lienard-Chipart Stability criterion,
Lin.Alg. Appl., (1989), 23-37.
[38] U. Helmke and P.A. Fuhrmann, Bezoutians,
Lin.Alg. Appl., (1989), vols. 122-124, 1039-1097 .
[37] P.A. Fuhrmann, Orthogonal matrix polynomials and
system theory, Rend. Sem. Mat. Univers. Politecn. Torino, Special Issue on
Control Theory,(1988), 68-124.
[36] P.A. Fuhrmann, Block Hankel matrix inversion - the
polynomial approach, in Proceedings of Amsterdam workshop on Operator Theory
and Applications, Birkhauser Verlag, 1986, 207-230.
[35] P.A. Fuhrmann, Remarks on the inversion
of Hankel matrices, Lin. Alg. Appl., (1986), 89-104.
[34] P.A. Fuhrmann, and P. S. Krishnaprasad, Towards a cell decomposition
for $Rat(n)$, IMA J. Math. Contr.,Info.3 (1986), 137-150.
[33] P.A. Fuhrmann, The algebraic Riccati equation - a
polynomial approach, Systems and Control Letters., 5 (1985), 369-376.
[32] T. Shamir and P.A. Fuhrmann, Minimal
factorizations of rational matrix functions in terms of polynomial models, Lin.
Alg. Appl., (1985),67-91.
[31] P.A. Fuhrmann, A matrix Euclidean
algorithm and matrix continued fractions, Systems and Control Letters., 3
(1983), 263-271.
[30] P.A. Fuhrmann, On Hamiltonian transfer
functions, Lin. Alg. Appl.,(1984), 1-93.
[29] P.A. Fuhrmann, On symmetric rational matrix
functions, Lin. Alg.Appl., Special issue on Linear Control Theory, (1983),
167-250.
[28] P.A. Fuhrmann, Transfer function reducibility, Systems
and Control Letters, 1 (1981), 116-118.
[27] P.A. Fuhrmann, Duality in polynomial models
with some applications to geometric control theory, IEEE Trans. Aut. Control,
AC-26 (1981), 284-295.
[26] P.A. Fuhrmann and J.C. Willems, A study of
(A,B)-invariant subspaces via polynomial models Int. J. Contr., 31 (1980),
467-494.
[25] P.A. Fuhrmann and J.C. Willems, Factorization indices
at infinity for rational matrix functions Integral Eq. and Oper. Th., 2 (1979),
287-301.
[24] P.A. Fuhrmann, Operator measures, selfadjoint
operators and dynamical systems, SIAM J. Math. Anal., 11 (1980), 737-757.
[23] P.A. Fuhrmann, Linear feedback via polynomial
models, Int. J. Contr.,30 (1979), 363-377.
[22] P.A. Fuhrmann, Simulation of linear systems
and factorization of matrix polynomials, Int. J. Control, 28 (1978), 689-705.
[21] P.A. Fuhrmann, On strict system equivalence
and similarity, Int.J. Contr., 25, 5-10.
[20] P.A. Fuhrmann, Algebraic system theory:
An analyst's point of view, J. Franklin Inst., 301 (1976), 521-540.
[19] P.A. Fuhrmann, On Hankel Operator ranges, meromorphic
pseudocontinuations and factorizations of operator valued analyic functions, J.
London Math.Soc., Series II, 13 (1976), 323-327.
[18] P.A. Fuhrmann, Exact controllability and observability
and realization theory in Hilbert space, J. Math. Anal. Appl., 53 (1976),
377-392.
[17] I.Y. Bar Itzhack, J. Meyer and P.A. Fuhrmann,
Strapdown matrix orthogonalizaton: The dual iterative algorithm IEEE Trans.
Aero. and Elect.Systems, AES-12 (1976), 32-38.
[16] P.A. Fuhrmann, On series and parallel coupling of a
class of discrete time infinite dimensional linear systems, SIAM J. Contr.
Optim., 14 (1976),339-358.
[15] P.A. Fuhrmann and R.W. Brockett, Normal symmetric
dynamical systems,SIAM J. Control, 14 (1976), 107-119.
[14] P.A. Fuhrmann, On J-symmetric restricted shifts,
Proc. Amer. Math.Soc., 5 (1975), 421-426.
[13] P.A. Fuhrmann, On controllability and observability of
systems connected in parallel, IEEE Trans. Circuits and Systems, CAS-22 (1975),
57.
[12] P.A. Fuhrmann, On generalized Hankel operators induced
by sums and products, Israel J. Math., 21 (1975), 279-295.
[11] P.A. Fuhrmann, Realization theory in Hilbert space for
a class of transfer functions, J. Functional Analysis, 18 (1975), 338-349.
[10] P.A. Fuhrmann, On realization of linear systems and
applications to some questions of stability, Math. System Th., 8 (1975),
132-142.
[9] P.A. Fuhrmann, Some results on controllability,
Ricerche di Automatica,5 (1974), 1-5.
[8] J. S. Baras and R. W. Brockett and P.A. Fuhrmann, A
state space approach for modelling infinite dimensional systems, IEEE Special
issue on System Identification and Time Series Analysis AC-19 (1974), 693-700.
[7] P.A. Fuhrmann, On sums of Hankel operators,
Proc. Amer. Math. Soc.,49 (1974), 1-4.
[6] P.A. Fuhrmann, On a class of finite dimensional
contractive perturbations of restricted shifts of finite multiplicity, Israel
J. Math., 16 (1974),162-175.
[5] P.A. Fuhrmann, On observability and stability in
infinite dimensional linear systems, J. Opt. Th. Appl., 12 (1973), 173-181.
[4] P.A. Fuhrmann, On weak and strong reachability and
controllability of infinite dimensional linear systems, J. Opt. Th. Appl., 12
(1972), 77-89.
[3] P.A. Fuhrmann, On maximal ideals in two algebras of
operator valued analytic functions, Israel J. Math., 8 (1970), 23-27.
[2] P.A. Fuhrmann, A functional calculus in Hilbert space
based on operator valued analytic functions, Israel J. Math., 6 (1968),
267-278.
[1] P.A. Fuhrmann, On the corona problem and its
application to spectral problems in Hilbert space, Trans. Amer. Math. Soc., 132
(1968), 55-67.
Conference and
Symposia Proceedings:
[14] P.A. Fuhrmann, On some uses of factorizations in linear
system theory, Proceedings of IFAC Conference on System Structure and Control,
Nantes, 1995.
[13] A. Gombani and P.A. Fuhrmann, On external
spectralfactors and geometric control, Proceedings of CDC Conference, ??, 199?.
[12] P.A. Fuhrmann, A class of characteristic
functionsand their system applications, Proc. MTNS 1993, Regensburg, vol. I,
135-158.
[11] J. Hoffmann and P.A. Fuhrmann, Positive real
balancingand orthogonal polynomials, Proc. MTNS 1993, Regensburg, vol. II,
227-230.
[10] P.A. Fuhrmann and U. Helmke, Output feedback
invariantsand canonical forms for linear dynamical systems, Proc. MTNS 1987,
Phoenix,Arizona.
[9] P.A. Fuhrmann, On the partial realization problem and the
recursiveinversion of Hankel and Toeplitz matrices, Contemporary Mathematics,
v.47; "Linear Algebra and its Role in System Theory", Amer. Math.
Soc., B. N. Datta - Editor, v.47, 149-161.
[8] P.A. Fuhrmann, Polynomial models and algebraic stability
criteria,Proceedings of Joint Workshop on Synthesis of Linear and Nonlinear
Systems,Bielefeld June 1981, 78-90.
[7] M.L.J. Hautus and P.A. Fuhrmann, On the zero module of rational matrix
functions, Proceedings CDC Conference Albuquerque, 1980.
[6] P.A. Fuhrmann, Functional models, factorizations and linear
systems,Proceedings of the NATO Advanced Study Institute on Algebraic and
GeometricMethods in Linear System Theory , Harvard University June 1979,
GeometricalMethods for the Theory of Linear Systems Edited by C. I. Byrnes and
C.F. Martin, D. Reidel 1980, 257-282.
[5] P.A. Fuhrmann, An integrative approach to linear system theory,Proc. of
the International Symposium on Mathematical Theory of Networks and Systems},
Delft July 1979, 2-13, Western Periodicals Co.
[4] P.A. Fuhrmann, On spectral minimality and fine structure of theshift
realization, Distributed parameter systems: Modelling and Identification,
Proceedings of the IFIP working conference, Rome 1976, Lecture Notes InControl
and Information Sciences 1, Springer Verlag.
[3] P.A. Fuhrmann, Algebraic ideas in infinite dimensional system
theory,Udine 1975, Lecture Notes in Economics and Mathematical Systems, vol.
13Springer Verlag 1976, 237-251.
[2] P.A. Fuhrmann, On canonical realization of sums and products
ofnonrational transfer functions, Proc. of the 8th Princeton Conference on
Information Sciences and Systems, 1974, 213-217.
[1] P.A. Fuhrmann, On a class of multi input-output control systemsin
Hilbert space, Proc. 11th Allerton Conference on Circuit and System Theory,
1973, 30-35.
Lecture Notes:
This
is a set of lecture notes prepared for the 1998 Thematic Term on Linear Algebra
and Control Theory, that took place at CIM, Coimbra,Portugal.
Slide sets:
For
the convenience of interested users, I am including several sets ofslides that
I have used at various conferences. Please point out to meany mistakes that you
may find. Remember: Nothing is perfect.
- This is a set of slides prepared for the IFAC Workshop
on System Structureand Control that took place in Nantes, 1995. Its
central themes arefactorizationand geometric
control theory.
- This is a set of slides based on [54]. It deals with
the parametrizationof the set of all minimal, not necessarily stable, spectralfactors.
- This is a set of slides prepared for the 1997 GAMM
meeting in Regensburg.It is based on some joint work with Andrea Gombani
and focuses ongeometriccontrolfrom a
functional point of view.
- This set of slides was prepared for the 1997 Toeplitz
Conference at TelAviv University. It reviews some applications of Toeplitzoperators to system theoretic
problems. Parts are based on joint workwith Uwe Helmke, see [59].
This is a set of slides prepared for the 1997
Summer Workshop on"Mathematicsfor Systems",St.
Emilion, France.
This is a set of slides prepared for the 1998
Thematic Term on LinearAlgebra and Control Theory, to take place at CIM, "Coimbra,"Portugal.
Some Photos:
With John Baras, in Roger Brockett's yard, Lexington
MA, 1977.
Mtzad Zohar, a border fortress on the way to the
Dead Sea.
NATO Conference, Cambridge MA, 1978.
The end of a memorable Massada climb by Michiel
Hazewinkel and T.J. Tarn, MTNS83.
Bob Hunt, PF and Edmund Jonckheere, PatrickDewilde, PF and Yves
Genin, De Branges and Gianni Marchesini, Roger Brockett, Gianni and Leonardo Marchesini, Jan van Schuppen,
GiorgioPicci, Zames, MTNS83.
P. Fuhrmann, Bucharest 1986.
B. Sz.-Nagy and P. Fuhrmann, Negev 19??.
Kalman and some of his students, (L.to R.:
E. Sontag, Y. Yamamoto, T. Matsuo and A.C. Antoulas). Kalman
and Lions, Kalman and PF, GiorgioPicci, Roger
Brockett and Jan Willems,, Brockett, Baras
and Gohberg,Michel Fliess (withJan Willems and
Michael Heymann in the background),
grouppicture, Frascatti 1990.
Raimund Ober,
AndersLindquist,Hector Sussmann facing the
Judeandesert
Tosio Ando, Adamjanand
Arov,Daniel Alpay and A. Dijksma, HarryDym and Rien Kaashoek,
Ciprian Foias andBill Helton,Harm Bart, AndreRan, A. Nudelman, I.
Gohberg and D. Arov,Heinz Langer, Sapporo 1991.
Thanos Antoulas in Kyoto,, R.Barmish and Pramod Khargonekar, , HidenoriKimura and guests, Kobe 1991.
Luciano Pandolfi, Grouppicture
at the Riccati Conference, Como.
Group picture at the ILAS meeting in Auburn.
Peli (Pratzel-Wolters)and UweHelmke at the Dead sea.Uwe Helmke afew years younger.PF and Raimund Ober on Massada.
Group picture at the ILAS meeting in
Chemnitz,August 1996.
Hans Schumacher and Peter Zagalak, PFand Anton Stoorvogel, Kharitonov
and AntonStoorvogel, Istanbul 1995.
Vladimir Kucera, 1996.
With Michiel Hazewinkel having coffee withthe
bedouins, December 1996.
Our bedouin hostess, December 1996.
The Operator Theory Conference in honour of Moshe Livsic, BGU 1997.
M. Livsic
The organizers: V. Vinnikov and D.Alpay
V. Adamyan , S.Fedorov, V. Adamyan and V. Dubovoy , A.Benartzy ,C. Davis ,
L.Debranges ,L. Debranges , H.de Snoo ,P. Dewilde and A. Markus ,P.Dewilde and P. Fuhrmann ,M. Dritschel, V.Adamyan, V. Dubovoy and A. Nudelman, A.Gombani ,
A. Kheifetz, A. Nudelman, M. Solomyak,V.
Vasyunin
J. Leblond, C. Sadosky, Ch. Tretter
S. Marcantognini
D. Hershkowitz , A.Kheifets ,N. Krupnik , H.Langer ,J. Leblond , B.Pavlov and V. Katsnelson ,S. Marcantognini ,A.Markus and P. Dewilde ,I. Lewkovitzand N. Cohen ,A. Nudelman, A.Nudelman and L. Sakhnovich,R. Ober ,R.Ober
, B. Pavlov ,J.Leblond, C. Sadoski and Ch. Tretter ,L.Sakhnovich , M. Solomyak ,A.Strauss , V. Tkachenko ,E.Tsekanovskii, S. Treill and V. Vasyunin ,V.Dubovoy, A. Nudelman and S. Treill ,E.Tsekanovskii, V. Vinnikov , L.Waksman ,N. Young and V. Vinnikov ,N.Young ,
St. Emilion Workshop, July 1997.
St. Emilion Workshop members at the
Smith Haut Lafitte winery, Bordeaux 1997.
Dinner at the Smith Haut Lafitte winery,
Bordeaux 1997.
Dinner at the Smith Haut Lafitte winery,
Bordeaux 1997.
Tom Kailath, Bordeaux 1997.
Paul Fuhrmann, Maho Najim, Tom Kailath.
Harry Dym, Bordeaux 1997.
Pictures taken at the conference in honor
of M.S. Livsic's 80th birthday, June-July 1997.
Pictures taken at the Kaiserslautern Conference, September
1997.
Pictures taken at the the thematic term on
Linear Algebra and Control, Coimbra, May-June 1998.
Pictures taken at the Padova MTNS-98,July
1998.
Israel Gohberg's 70th Birtday Conference, Beer Sheva, 1998.
D. Hinrichsen's 60th birthday Conference,
April 1999, Borkum Island
6th INTERNATIONAL CONFERENCE ON
OPTIMIZATIONAND APPROXIMATION, GUATEMALA CITY, MARCH 2001
Shaul Fuhrmann
Naomi Fuhrmann
![[1] P.A. Fuhrmann, Linear Operators and Systems in Hilbert Space, McGraw-Hill, New York 1981.](los.jpg){kind=link}
![[2] P.A. Fuhrmann, Editor, Proceedings of International Symposium on the Mathematical Theory of Networks and Systems, MTNS-83,Springer, Berlin 1984.](book.gif){kind=link}
