P. K. Asea and P. J. Zak, Time-to-build and cycles, Journal of Economic Dynamics and Control, vol.23, issue.8, pp.1155-1175, 1999.
DOI : 10.1016/S0165-1889(98)00052-9

M. Bambi, Endogenous growth and time-to-build: The AK case, Journal of Economic Dynamics and Control, vol.32, issue.4, pp.1015-1040, 2008.
DOI : 10.1016/j.jedc.2007.04.002

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.9746

M. Bambi, G. Fabbri, and F. Gozzi, Optimal policy and consumption smoothing effects in the time-tobuild AK model, Munich Personal RePEc Archive, 2009.

V. Barbu and G. Da-prato, Hamilton-Jacobi equations in Hilbert spaces; variational and semigroup approach, Annali di Matematica Pura e Applicata, pp.303-349, 1985.
DOI : 10.1007/BF01766599

V. Barbu and G. Da-prato, A note on a Hamilton-Jacobi equation in Hilbert space, Nonlinear Analysis, pp.1337-1345, 1985.

V. Barbu, G. Da-prato, and C. Popa, Existence and uniqueness of the dynamic programming equation in Hilbert space, Nonlinear Analysis: Theory, Methods & Applications, vol.7, issue.3, pp.283-299, 1983.
DOI : 10.1016/0362-546X(83)90073-1

V. Barbu and P. Th, Convexity and Optimization in Banach Spaces, Editura Academiei, 1986.

M. Bardi, C. Dolcetta, and I. , Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, 1997.
DOI : 10.1007/978-0-8176-4755-1

R. Bekes, The range of convolution operators, Pacific Journal of Mathematics, vol.110, issue.2, pp.257-271, 1984.
DOI : 10.2140/pjm.1984.110.257

A. Bensoussan, G. Da-prato, M. C. Delfour, and S. K. Mitter, Representation and Control of Infinite Dimensional System, 2007.

R. Boucekkine, O. Licandro, P. Luis, A. , F. Del-rio et al., Vintage capital and the dynamics of the AK model, Journal of Economic Theory, vol.120, issue.1, pp.39-72, 2005.
DOI : 10.1016/j.jet.2004.02.006

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2010.
DOI : 10.1007/978-0-387-70914-7

P. Cannarsa, Regularity properties of solutions to Hamilton-Jacobi-Bellman equations in infinite dimensions and nonlinear optimal control, Differential and Integral Equations, pp.479-493, 1989.

P. Cannarsa, D. Blasio, and G. , A direct approach to infinite dimensional Hamilton?Jacobi equations and applications to convex control with state constraints, Differential and Integral Equations, vol.8, issue.2, pp.225-246, 1995.

P. Cannarsa, D. Blasio, and G. , Dynamic programming for an abstract second order evolution equation with convex state constraints, Control of Partial Differential Equations, IFIP WG 7.2 Conference, Villa Madruzzo, 1993.

P. Cannarsa and H. M. Soner, Generalized one-sided estimates for solutions of Hamilton-Jacobi equations and applications, Nonlinear Analysis: Theory, Methods & Applications, vol.13, issue.3, pp.305-323, 1989.
DOI : 10.1016/0362-546X(89)90056-4

E. B. Davies, One-parameter semigroups, 1980.
DOI : 10.1017/CBO9780511618864.007

D. Blasio and G. , Global solutions for a class of Hamilton-Jacobi equations in Hilbert spaces, Numerical Functional Analysis and Optimization, pp.261-30086, 1985.

D. Blasio and G. , Optimal Control with Infinite Horizon for Distributed Parameter Systems with Constrained Controls, SIAM Journal on Control and Optimization, vol.29, issue.4, pp.909-925, 1991.
DOI : 10.1137/0329050

I. Ekeland and R. Temam, Convex Analysis and Variational Problem, 1976.
DOI : 10.1137/1.9781611971088

K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 2000.
DOI : 10.1007/s002330010042

G. Fabbri and F. Gozzi, Solving optimal growth models with vintage capital: The dynamic programming approach, Journal of Economic Theory, vol.143, issue.1, pp.331-373, 2008.
DOI : 10.1016/j.jet.2008.03.008

G. Fabbri, F. Gozzi, and A. Swiech, Verification Theorems and construction of ?-optimal controls, Journal of Convex Analysis, vol.17, issue.2, pp.611-642, 2010.

S. Faggian, Regular Solutions of First-Order Hamilton?Jacobi Equations for Boundary Control Problems and Applications to Economics, Applied Mathematics and Optimization, vol.51, issue.2, pp.123-162, 2005.
DOI : 10.1007/s00245-004-0809-z

S. Faggian, Hamilton???Jacobi Equations Arising from Boundary Control Problems with State Constraints, SIAM Journal on Control and Optimization, vol.47, issue.4, pp.2157-2178, 2008.
DOI : 10.1137/070683738

S. Federico, B. Goldys, and F. Gozzi, HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, I: Regularity of Viscosity Solutions, SIAM Journal on Control and Optimization, vol.48, issue.8, pp.4821-5546, 2010.
DOI : 10.1137/09076742X

S. Federico, B. Goldys, and F. Gozzi, HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Verification and Optimal Feedbacks, SIAM Journal on Control and Optimization, vol.49, issue.6, 2011.
DOI : 10.1137/100804292

URL : https://hal.archives-ouvertes.fr/hal-00583124

G. Feichtinger, R. Hartl, and S. Sethi, Dynamic Optimal Control Models in Advertising: Recent Developments, Management Science, vol.40, issue.2, pp.195-226, 1994.
DOI : 10.1287/mnsc.40.2.195

F. Gozzi, Some Results for an Optimal Control Problem with Semilinear State Equation, SIAM Journal on Control and Optimization, vol.29, issue.4, pp.751-768, 1991.
DOI : 10.1137/0329041

F. Gozzi, Some results for an infinite horizon control problem governed by a semilinear state equation, Proceedings Vorau, pp.145-163, 1988.

F. Gozzi and C. Marinelli, Stochastic Optimal Control of Delay Equations Arising in Advertising Models, Stochastic PDEs and Applications VII. Levico, pp.133-148, 2004.
DOI : 10.1201/9781420028720.ch13

F. Gozzi, C. Marinelli, and S. Savin, On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with??Memory Effects, Journal of Optimization Theory and Applications, vol.21, issue.3, pp.291-321, 2009.
DOI : 10.1007/s10957-009-9524-5

A. Ichikawa, Quadratic Control of Evolution Equations with Delays in Control, SIAM Journal on Control and Optimization, vol.20, issue.5, 1982.
DOI : 10.1137/0320048

H. N. Koivo and E. B. Lee, Controller synthesis for linear systems with retarded state and control variables and quadratic cost, Automatica, vol.8, issue.2, pp.203-208, 1972.
DOI : 10.1016/0005-1098(72)90068-4

F. E. Kydland and E. C. Prescott, Time to Build and Aggregate Fluctuations, Econometrica, vol.50, issue.6, pp.1345-1370, 1982.
DOI : 10.2307/1913386

X. Li and J. Yong, Optimal Control Theory for Infinite-Dimensional Systems, 1995.
DOI : 10.1007/978-1-4612-4260-4

M. Nerlove and J. K. Arrow, Optimal Advertising Policy under Dynamic Conditions, Economica, vol.29, issue.114, pp.129-142, 1962.
DOI : 10.2307/2551549

W. Pauwels, Optimal dynamic advertising policies in the presence of continuously distributed time lags, Journal of Optimization Theory and Applications, vol.29, issue.1, pp.79-89, 1977.
DOI : 10.1007/BF00936722

R. Phelps, Convex Functions, Monotone operators and Differentiability, Lecture Notes in Mathematics, vol.1364, 1993.
DOI : 10.1007/978-3-662-21569-2

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

S. P. Sethi, Sufficient Conditions for the Optimal Control of a Class of Systems with Continuous Lags, Journal of Optimization Theory and Applications, vol.13, issue.5, 1974.

J. Tsoukalas, Time to build capital: Revisiting investment-cash-flow sensitivities, Journal of Economic Dynamics and Control, vol.35, issue.7, 2010.
DOI : 10.1016/j.jedc.2010.12.009

R. B. Vinter and R. H. Kwong, The infinite dimensional quadratic control problem for linear systems with state and control delay: an evolution equation approach, SIAM Journal on control and optimization, vol.19, issue.1, 1981.

J. Yong and X. Y. Zhou, Stochastic Controls -Hamiltonian Systems and HJB equations, 1999.