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Paul A. Fuhrmann

Welcome to my homepage; It is still under construction, so please excuse the mess.

Under Construction

Sde Boker Workshop


comments may be addressed to fuhrmannbgu@gmail.com 


Department of Mathematics,

Ben-Gurion University of the Negev,

POB 653. Beer-Sheva 84105,


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.


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.





[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.


[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 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


Shaul Fuhrmann
Naomi Fuhrmann