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2011 | 9 | 2 | 205-243
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Fredholm determinants

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
2
Strony
205-243
Opis fizyczny
Daty
wydano
2011-04-01
online
2011-02-18
Twórcy
autor
  • CIMS
Bibliografia
  • [1] Ahlfors L.V., Complex Analysis, Internat. Ser. Pure Appl. Math., 3rd ed., McGraw-Hill, New York, 1979
  • [2] Brown R., A brief account of microscopical observations made in the months of June, July, and August, 1827, on the particles contained in the pollen of plants, etc., Philosophical Magazine, 1828, 4, 161–173
  • [3] Cameron R.H., Martin W.T., The Wiener measure of Hilbert neighborhoods in the space of real continuous functions, Journal of Mathematics and Physics Mass. Inst. Tech., 1944, 23, 195–209
  • [4] Conrey J.B., The Riemann hypothesis, Notices Amer. Math. Soc., 2003, 50(3), 341–353
  • [5] Courant R., Differential and Integral Calculus, vol. 2, Wiley Classics Lib., John Wiley & Sons, New York, 1988
  • [6] Courant R., Hilbert D., Methoden der Mathematischen Physik, Springer, Berlin, 1931
  • [7] Dyson F.J., Statistical theory of the energy levels of complex systems. I, J. Mathematical Phys., 1962, 3, 140–156 http://dx.doi.org/10.1063/1.1703773
  • [8] Dyson F.J., Fredholm determinants and inverse scattering problems, Comm. Math. Phys., 1976, 47(2), 171–183 http://dx.doi.org/10.1007/BF01608375
  • [9] Einstein A., Über die von der molekularkinetischen Theorie der Wärme gefordete Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys., 1905, 17, 549–560; reprinted in: Investigations on the Theory of the Brownian Movement, Dover, New York, 1956 http://dx.doi.org/10.1002/andp.19053220806
  • [10] Fredholm I., Sur une classe d’équations fonctionelles, Acta Math., 1903, 27(1), 365–390 http://dx.doi.org/10.1007/BF02421317
  • [11] Gardner C.S., Greene J.M., Kruskal M.D., Miura R.M., Methods for solving the Korteweg-deVries equation, Phys. Rev. Lett., 19(19), 1967, 1095–1097 http://dx.doi.org/10.1103/PhysRevLett.19.1095
  • [12] Jimbo M., Miwa T., Môri Y., Sato M., Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent, Phys. D, 1980, 1(1), 80–158 http://dx.doi.org/10.1016/0167-2789(80)90006-8
  • [13] Kato T., A Short Introduction to Perturbation Theory for Linear Operators, Springer, New York-Berlin, 1982
  • [14] Lamb G.L., Jr., Elements of Soliton Theory, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 1980
  • [15] Lax P.D., Linear Algebra, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 1997
  • [16] Lax P.D., Functional Analysis, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 2002
  • [17] Lévy P., Le Mouvement Brownien, Mémoir. Sci. Math., 126, Gauthier-Villars, Paris, 1954
  • [18] McKean H.P., Jr., Stochastic Integrals, Probab. Math. Statist., Academic Press, New York-London, 1969
  • [19] Mehta M.L., Random Matrices, 2nd ed., Academic Press, Boston, 1991
  • [20] Munroe M.E., Introduction to Measure and Integration, Addison-Wesley, Cambridge, 1953
  • [21] Pöppe Ch., The Fredholm determinant method for the KdV equations, Phys. D, 1984, 13(1–2), 137–160 http://dx.doi.org/10.1016/0167-2789(84)90274-4
  • [22] Tracy C.A., Widom H., Introduction to random matrices, In: Geometric and Quantum Aspects of Integrable Systems, Scheveningen, 1992, Lecture Notes in Phys., 424, Springer, Berlin, 1993, 103–130 http://dx.doi.org/10.1007/BFb0021444
  • [23] Uhlenbeck G.E., Ornstein L.S., On the theory of the Brownian motion, Phys. Rev., 1930, 36, 823–841 http://dx.doi.org/10.1103/PhysRev.36.823
  • [24] Weyl H., The Classical Groups, Princeton University Press, Princeton, 1939
  • [25] Whittaker E.T., Watson G.N., A Course of Modern Analysis, 4th ed., Cambridge University Press, New York, 1962
  • [26] Wiener N., Differential space, Journal of Mathematics and Physics Mass. Inst. Tech., 1923, 2, 131–174
  • [27] Wigner E., On the distribution of the roots of certain symmetric matrices, Ann. of Math., 1958, 67, 325–326 http://dx.doi.org/10.2307/1970008
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0003-5
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