Surjectivity of differential operators and linear topological invariants for spaces of zero solutions

Thomas Kalmes1
1Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany

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 range of convolution operators. Ann. Math. 76, 148–170 (1962)

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)