Nonlinear Equations with Infinitely many Derivatives

Abraham R., Marsden J.E., Ratiu T.: Manifolds, Tensor Analysis, and Applications, 2nd edn. Springer, Berlin (1988)

Arendt W., Batty C.J.K., Hieber M., Neubrander F.: Vector-valued Laplace transforms and Cauchy problems. Birkhäuser, Basel (2001)

Barnaby, N., Kamran, N.: Dynamics with infinitely many derivatives: the initial value problem. J. High Energy Phys. 2008 no. 02, Paper 008, 40 pp

Barnaby, N., Kamran, N.: Dynamics with infinitely many derivatives: variable coefficient equations. J. High Energy Phys. 2008 no. 12, Paper 022, 27 pp

Bartkowski K., Górka P.: One-dimensional Klein–Gordon equation with logarithmic nonlinearities. J. Phys. A 41, 355201 (2008)

Calcagni G., Montobbio M., Nardelli G.: Route to nonlocal cosmology. Phys. Rev. D 76, 126001 (20 pages) (2007)

Calcagni G., Montobbio M., Nardelli G.: Localization of nonlocal theories. Phys. Lett. B 662, 285–289 (2008)

Dragovich B.: Zeta-nonlocal scalar fields. Theor. Math. Phys. 157, 1671–1677 (2008)

Dubinskii Yu.A.: The algebra of pseudodifferential operators with analytic symbols and its applications to mathematical physics. Russian Math. Surv. 37, 109–153 (1982)

Gerasimov, A.A., Shatashvili, S.L.: On exact tachyon potential in open string field theory. J. High Energy Phys. 2000, no. 10, Paper 34, 12 pp

Goodman R.: Analytic and entire vectors for representations of Lie groups. Trans. Am. Math. Soc. 143(3), 55–76 (1969)

Gorbachuk M.L., Mokrousov Yu.G.: Conditions for subspaces of analytic vectors of a closed operator in a Banach space to be dense. Funct. Anal. Appl. 35, 64–66 (2001)

Górka, P., Prado, H., Reyes, E.G.: Equations with infinitely many derivatives and string theory (2009, in preparation)

Hebey E., Vaugon M.: Sobolev spaces in the presence of symmetries. J. Math. Pures Appl. 76, 859–881 (1997)

Kostelecký V.A., Samuel S.: On a nonperturbative vacuum for the open bosonic string. Nucl. Phys. B 336, 263–296 (1990)

Lions P.-L.: Symmetry and compactness in Sobolev spaces. J. Funct. Anal. 49, 315–334 (1982)

Moeller, N., Zwiebach, B.: Dynamics with infinitely many time derivatives and rolling tachyons. J. High Energy Phys. 2002, no. 10, Paper 34, 38 pp

Rosenberg S.: The Laplacian on a Riemannian Manifold. Cambridge University Press, Cambridge (1997)

Stein, E.M., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton Mathematical Series, PUP, Princeton (1971)

Taylor M.E.: Partial Differential Equations. I. Basic Theory. Springer, New York (1996)

Taylor W.: String field theory. In: Oriti, D. (eds) Approaches to Quantum Gravity, pp. 210–228. Cambridge University Press, Cambridge (2009)

Van T.D., Hào D.N.: Differential operators of infinie order with real arguments and their applications. World Scientific, Singapore (1994)

Vladimirov V.S.: The equation of the p-adic open string for the scalar tachyon field. Izvestiya: Math. 69, 487–512 (2005)

Vladimirov, V.S., Volovich, Ya.I.: Nonlinear dynamics equation in p-adic string theory. Teoret. Mat. Fiz. 138 (2004), 355–368; English transl., Theoret. Math. Phys. 138, 297–309 (2004)

Vladimirov V.S., Volovich I.V., Zelenov E.I.: p-adic Analysis and Mathematical Physics. World Scientific, Singapore (1994)

Witten E.: Noncommutative geometry and string field theory. Nucl. Phys. B 268, 253–294 (1986)