Phương trình Volterra trừu tượng trong các không gian lồi địa phương

Albanese AA, Kühnemund F. Trotter-Kato approximation theorems for locally equicontinuous semigroups. Riv Mat Univ Parma, 2002, 1: 19–53 Albanese A A, Mangino E. Trotter-Kato approximation theorems for bi-continuous semigroups and applications to Feller semigroups. J Math Anal Appl, 2004, 289: 477–492 Arendt W, Batty C J K, Hieber M, et al. Vector-Valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics. Basel: Birkhäuser Verlag, 2 2001 Arendt W, El-Mennaoui O, Keyantuo V. Local integrated semigroups: evolution with jumps of regularity. J Math Anal Appl, 1994, 186: 572–595 Arendt W, Nikolski N. Vector-valued holomorphic functions revisited. Math Z, 2000, 234: 777–805 Barbu V. Differentiable distribution semi-groups. Ann Scuola Norm Sup Pisa Cl Sci, 1969, 23: 413–429 Barletta E, Dragomir S. Vector valued holomorphic functions. Bull Math Soc Sci Math Roumanie, 2009, 52: 211–226 Bazhlekova E. Fractional Evolution Equations in Banach Spaces. PhD dissertation. Eindhoven: Eindhoven University of Technology, 2001 Beals R. On the abstract Cauchy problem. J Funct Anal, 1972, 10: 281–299 Chill R, Keyantuo V, Warma M. Generation of cosine families on L p(0, 1) by elliptic operators with Robin boundary conditions. In: Functional Analysis and Evolution Equations. Basel: Birkhäuser Verlag, 2008, 113–130 Ciorănescu I, Lumer G. Problèmes d’évolution régularisés par un noyan général K(t). Form Formule de Duhamel, prolongements, théor`emes de génération. C R Acad Sci Paris Sér I Math, 1994, 319: 1273–1278 Ciorănescu I, Lumer G. Regularization of evolution equations via kernels K(t), K-evolution operators and convoluted semigroups, generation theorems. In: Seminar Notes in Functional Analysis and PDE. Baton Rouge: Louisiana State University, 1994, 45–52 Ciorănescu I. Beurling spaces of class (M p) and ultradistribution semi-groups. Bull Sci Math, 1978, 102: 167–192 Da Prato G, Sinestrari E. Differential operators with nondense domain. Ann Scuola Norm Sup Pisa Cl Sci, 1987, 14: 285–344 deLaubenfels R. Existence Families, Functional Calculi and Evolution Equations. In: Lecture Notes Math, vol. 1570. New York: Springer-Verlag, 1994 deLaubenfels R. Matrices of operators and regularized semigroups. Math Z, 1993, 212: 619–629 deLaubenfels R, Yao F, Wang S W. Fractional powers of operators of regularized type. J Math Anal Appl, 1996, 199: 910–933 Dembart B. On the theory of semigroups on locally convex spaces. J Funct Anal, 1974, 16: 123–160 Grosse-Erdmann K G. A weak criterion for weak holomorphy. Math Proc Camb Phil Soc, 2004, 136: 399–411 Hieber M, Holderrieth A, Neubrander F. Regularized semigroups and systems of linear partial differential equations. Ann Scuola Norm Sup Pisa, 1992, 19: 363–379 Jeong D H, Park J Y, Yu Y W. Exponentially equi-continuous C-semigroups in locally convex space. J Korean Math Soc, 1989, 26: 1–15 Jordá E. Vitali’s and Harnack’s type results for vector-valued functions. J Math Anal Appl, 2007, 327: 739–743 Kim M. Abstract Volterra Equations. PhD dissertation. Baton Rouge: Louisiana State University, 1995 Kim M. Trotter-Kato theorems for convoluted resolvent families. Commun Korean Math Soc, 2004, 19: 293–305 Kisyński J. The Petrovskiĭ correctness and semigroups of operators. Preprint, 2009 Komatsu H. Ultradistributions, I. Structure theorems and a characterization. J Fac Sci Univ Tokyo Sect IA Math, 1973, 20: 25–105 Komatsu H. Semi-groups of operators in locally convex spaces. J Math Soc Japan, 1964, 16: 230–262 Kōmura T. Semigroups of operators in locally convex spaces. J Funct Anal, 1968, 2: 258–296 Konishi Y. Cosine functions of operators in locally convex spaces. J Fac Sci Univ Tokyo Sect IA Math, 1971/72, 18: 443–463 Kostić M, Pilipović S. Convoluted C-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines. J Math Anal Appl, 2008, 338: 1224–1242 Kostić M. Differential and analytical properties of semigroups of linear operators. Integral Equations Operator Theory, 2009, 67: 499–557 Kostić M. Ill-posed abstract Volterra equations. Preprint, 2010 Kostić M. Generalized Semigroups and Cosine Functions. Belgrade: Mathematical Institute, 2011 Kostić M. (a, k)-regularized C-resolvent families: regularity and local properties. Abstr Appl Anal, 2009, Article ID 858242, 27 pages, 2009 Kunstmann P C. Stationary dense operators and generation of non-dense distribution semigroups. J Operator Theory, 1997, 37: 111–120 Lemle L D. L 1(ℝd, dx)-uniqueness of weak solutions for the Fokker-Planck equation associated with a class of Dirichlet operators. Electron Res Announc Math Sci, 2008, 15: 65–70 Li F B, Li M, Zheng Q. Fractional evolution equations governed by coercive differential operators. Abstr Appl Anal, 2009, Art. ID 438690, 14 pages Li Y C. Integrated C-Semigroups and C-Cosine Functions on Locally Convex Spaces. PhD dissertation. TaiPei: National Central University, 1991 Li Y C, Shaw S Y. N-times integrated C-semigroups and the abstract Cauchy problem. Taiwanese J Math, 1997, 1: 75–102 Li M, Zheng Q, Zhang J. Regularized resolvent families. Taiwanese J Math, 2007, 11: 117–133 Lizama C. Regularized solutions for abstract Volterra equations. J Math Anal Appl, 2000, 243: 278–292 Lizama C. On approximation and representation of K-regularized resolvent families. Integral Equations Operator Theory, 2001, 41: 223–229 Lizama C, Prado H. Rates of approximations and ergodic limits of regularized operator families. J Approx Theory, 2003, 122: 42–61 Lizama C, Sánchez J. On perturbation of K-regularized resolvent families. Taiwanese J Math, 2003, 7: 217–227 Lizama C, Prado H. On duality and spectral properties of (a, k)-regularized resolvents. Proc Roy Soc Edinburgh Sect A, 2009, 139: 505–517 Martinez C, Sanz M. The Theory of Fractional Powers of Operators. Amsterdam: North-Holland Math Stud, 2001 Meise R, Vogt D. Introduction to Functional Analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. New York: Oxford University Press, 1997 Müller M. Approximation of local convoluted semigroups. J Math Anal Appl, 2002, 269: 401–420 Moore R T. Generation of equicontinuous semigroups by hermitian and sectorial operators. I. Bull Amer Math Soc, 1971, 77: 224–229 Periago F, Straub B. A functional calculus for almost sectorial operators and applications to abstract evolution equations. J Evol Equ, 2002, 2: 41–68 Prüss J. Evolutionary Integral Equations and Applications. Monographs in Mathematics, 87. Basel: Birkhäuser Verlag, 1993 Prado H. On the asymptotic behavior of regularized operator families. Semigroup Forum, 2006, 73: 243–252 Schwartz L. Lectures on mixed problems in partial differential equations and the representation of semigroups. In: Tata Institute of Fundamental Research, Bombay, 1958 Straub B. Fractional powers of operators with polynomially bounded resolvent and the semigroups generated by them. Hiroshima Math J, 1994, 24: 529–548 Ushijima T. On the abstract Cauchy problem and semi-groups of linear operators in locally convex spaces. Sc Papers College Gen Ed Univ Tokyo, 1971, 21: 93–122 von Wahl W. Gebrochene potenzen eines elliptischen operators und parabolische differentialgleichungen in räumen Hölderstetiger funktionen.N Nachr Akad Wiss Göttingen Math-Phys Kl, 1972, 11: 231–2 Wu L, Zhang Y. A new topological approach to the L ∞-uniqueness of operators and L ∞-uniqueness of Fokker-Planck equations. J Funct Anal, 2006, 241: 557–610 Xiao T J, Liang J. The Cauchy Problem for Higher-Order Abstract Differential Equations. Berlin: Springer-Verlag, 1998 Xiao T J, Liang J. Abstract degenerate Cauchy problems in locally convex spaces. J Math Anal Appl, 2001, 259: 398–412 Xiao T J, Liang J. Approximations of Laplace transforms and integrated semigroups. J Funct Anal, 2000, 172: 202–220 Xiao T J, Liang J. Higher order degenerate Cauchy problems in locally convex spaces. Tübingen: Tübinger Berichte zur Funktionalanalysis, 2003 Yosida K. Holomorphic semigroups in a locally convex linear topological space. Osaka Math J, 1963, 15: 51–57 Zheng Q. Matrices of operators and regularized cosine functions. J Math Anal Appl, 2006, 315: 68–75 Zheng Q, Li Y. Abstract parabolic systems and regularized semigroups. Pacific J Math, 1998, 182: 183–199 Zheng Q. The analyticity of abstract parabolic and correct systems. Sci China Ser A, 2002, 45: 859–865