Surjectivity of differential operators and linear topological invariants for spaces of zero solutions
Tóm tắt
Từ khóa
Tài liệu tham khảo
Bonet, J., Domański, P.: Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences. J. Funct. Anal. 230, 329–381 (2006)
Bonet, J., Domański, P.: The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations. Adv. Math. 217(2), 561–585 (2008)
Domański, P.: Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives. In: Orlicz Centenary Volume, Banach Center Publications, vol. 64, pp. 51–70. Polish Academy Science, Warsaw (2004)
Domański, P.: Real analytic parameter dependence of solutions of differential equations. Rev. Mat. Iberoam. 26(1), 175–238 (2010)
Frerick, L., Kalmes, T.: Some results on surjectivity of augmented semi-elliptic differential operators. Math. Ann. 347, 81–94 (2010)
Grothendieck, A.: Sur les espaces de solution d’une classe générale d’equations aux dérivées partielles. J. Analyse Math. 2, 243–280 (1952–53)
Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Mem. Am. Math. Soc. 16, 140 (1955)
Hörmander, L.: On the existence and the regularity of solutions of linear pseudo-differential equations. Ens. Math. 17, 99–163 (1971)
Hörmander, L.: The Analysis of Linear Partial Differential Operators I and II. Springer, Berlin (1983)
Kalmes, T.: Every $$P$$ P -convex subset of $${\mathbb{R}}^2$$ R 2 is already strongly $$P$$ P -convex. Math. Z. 269(3–4), 721–731 (2011)
Kalmes, T.: Some results on surjectivity of augmented differential operators. J. Math. Anal. Appl. 386, 125–134 (2012)
Kalmes, T.: The augmented operator of a surjective partial differential operator with constant coefficients need not be surjective. Bull. Lond. Math. Soc. 44, 610–614 (2012)
Malgrange, B.: Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution. Ann. Inst. Fourier Grenoble 6, 271–355 (1955–1956)
Meise, R., Taylor, B.A., Vogt, D.: Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse. Ann. Inst. Fourier Grenoble 40(3), 619–655 (1990)
Meise, R., Taylor, B.A., Vogt, D.: Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces. Manuscr. Math. 90(4), 449–464 (1996)
Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (2004)
Nakane, S.: $$P$$ P -convexity with respect to differential operators which act on linear subspaces. Proc. Jpn. Acad. Ser. A Math. Sci. 55, 343–347 (1979)
Persson, J.: The wave operator and $$P$$ P -convexity. Boll. Un. Mat. Ital. (5) 18, 591–604 (1981)
Persson, J.: The geometry of $$P$$ P -convex sets. Boll. Un. Mat. Ital. (7) 7, 549–573 (1993)
Tintarev, K.: On the geometry of $$P$$ P -convex sets for operators of real principle type. Isr. J. Math. 64, 195–206 (1988)
Tintarev, K.: Characterization of $$P$$ P -convexity for supports in terms of tangent curves. J. Math. Anal. Appl. 164, 590–596 (1992)
Trèves, F.: Linear Partial Differential Operators with Constant Coefficients, Mathematics and Its Applications, vol. 6. Gordon and Breach Science Publishers, New York (1966)
Trèves, F.: Locally Convex Spaces and Linear Partial Differential Equations. Springer, Berlin (1967)
Trèves, F.: Topological Vector Spaces, Distributions, and Kernels. Academic Press, London (1967)
Vogt, D.: Subspaces and quotients of (s). In: Bierstedt, K.D., Fuchssteiner, B. (eds.) Functional Analysis: Survey and Recent Results, North-Holland Mathematics Studies, vol. 27, pp. 167–187. North-Holland Publishing Company, Amsterdam (1977)
Vogt, D., Wagner, M.J.: Charakterisierung der Quotientenräume von $$s$$ s und eine Vermutung von Martineau. Studia Math. 68, 225–240 (1980)
Vogt, D.: On the solvability of $$P(D)f=g$$ P ( D ) f = g for vector valued functions. RIMS Kokyoroku 508, 168–181 (1983)
Vogt, D.: Sequence space representations of spaces of test functions and distributions. In: Functional Analysis, Holomorphy, and Approximation Theory (Rio de Janeiro, 1979), Volume 83 of Lecture Notes in Pure and Applied Mathematics, pp. 405–443. Dekker, New York (1983)
Vogt, D.: Invariants and spaces of zero solutions of linear partial differential operators. Arch. Math. 87, 163–171 (2006)
Wiechert, G.: Dualitäts- und Strukturtheorie der Kerne von linearen Differentialoperatoren, Dissertation Wuppertal (1982)
Zachmanoglou, E.C.: An application of Holmgren’s theorem and convexity with respect to differential operators with flat characteristic cones. Trans. Am. Math. Soc. 140, 109–115 (1969)