zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On boundary values of fractional resolvent families. (English) Zbl 1230.47071
Authors’ abstract: Boundary values of analytic fractional resolvent families are deduced via the approximation of fractional powers of operators, and square root reductions of fractional resolvent families are given as well.
47D03(Semi)groups of linear operators
26A33Fractional derivatives and integrals (real functions)
[1]Arendt, W.; Batty, C. J. K.; Hieber, M.; Neubrander, F.: Vector-valued Laplace transforms and Cauchy problems, (2001)
[2]Baeumer, B.; Meerschaert, M. M.; Nane, E.: Brownian subordinators and fractional Cauchy problems, Trans. amer. Math. soc. 361, 3915-3930 (2009) · Zbl 1186.60079 · doi:10.1090/S0002-9947-09-04678-9
[3]E. Bajlekova, Fractional evolution equations in Banach spaces, PhD thesis, Eindhoven University of Technology, 2001. · Zbl 0989.34002
[4]Benson, D. A.; Wheatcraft, S. W.; Meerschaert, M. M.: The fractional-order governing equation of Lévy motion, Water resour. Res 36, No. 6, 1413-1424 (2000)
[5]Chen, C.; Li, M.: On fractional resolvent operator functions, Semigroup forum 80, 121-142 (2010) · Zbl 1185.47040 · doi:10.1007/s00233-009-9184-7
[6]Cioranescu, I.; Keyantuo, V.: On operator cosine functions in UMD spaces, Semigroup forum 63, 429-440 (2001) · Zbl 1191.47056 · doi:10.1007/s002330010086
[7]Da Prato, G.; Iannelli, M.: Linear integrodifferential equations in Banach space, Rend. sem. Mat. univ. Padova 62, 207-219 (1980) · Zbl 0451.45014 · doi:numdam:RSMUP_1980__62__207_0
[8]Fattorini, H. O.: Ordinary differential equations in linear topological spaces II, J. differential equations 6, 50-70 (1969) · Zbl 0181.42801 · doi:10.1016/0022-0396(69)90117-X
[9]Fattorini, H. O.: Uniformly bounded cosine functions in Hilbert space, Indiana univ. Math. J. 20, 411-425 (1970/1971) · Zbl 0185.38501 · doi:10.1512/iumj.1970.20.20035
[10]Haase, M.: The functional calculus for sectorial operators, (2006)
[11]Haase, M.: The group reduction for bounded cosine functions on UMD spaces, Math. Z. 262, 281-299 (2009) · Zbl 1172.47031 · doi:10.1007/s00209-008-0373-y
[12]Hörmander, L.: Estimates for translation invariant operators in lp spaces, Acta math. 104, 93-139 (1960) · Zbl 0093.11402 · doi:10.1007/BF02547187
[13]Karczewska, A.; Lizama, C.: Stochastic Volterra equations driven by cylindrical weiner process, J. evol. Equ. 7, 373-386 (2007) · Zbl 1120.60062 · doi:10.1007/s00028-007-0302-2
[14]Keyantuo, V.; Lizama, C.; Miana, P. J.: Algebra homomorphisms defined via convoluted semigroups and cosine functions, J. funct. Anal. 257, 3454-3487 (2009) · Zbl 1190.47045 · doi:10.1016/j.jfa.2009.07.017
[15]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[16]Kostić, M.: (a,k)-regularized C-resolvent families: regularity and local properties, Abstr. appl. Anal. 2009 (2009) · Zbl 1200.47059 · doi:10.1155/2009/858242
[17]Li, M.; Chen, C.; Li, Fu-Bo: On fractional powers of generators of fractional resolvent families, J. funct. Anal. 259, No. 10, 2702-2726 (2010) · Zbl 1203.47021 · doi:10.1016/j.jfa.2010.07.007
[18]Li, M.; Zheng, Q.: On spectral inclusions and approximations of α-times resolvent families, Semigroup forum 69, 356-368 (2004) · Zbl 1096.47516 · doi:10.1007/s00233-004-0128-y
[19]Li, M.; Zheng, Q.; Zhang, J.: Regularized resolvent families, Taiwanese J. Math. 11, 117-133 (2007) · Zbl 1157.45006
[20]Lizama, C.: Regularized solutions for abstract Volterra equations, J. math. Anal. appl. 243, 278-292 (2000) · Zbl 0952.45005 · doi:10.1006/jmaa.1999.6668
[21]Martínez, C.; Sanz, M.: The theory of fractional powers of operators, North-holland math. Stud. 187 (2001)
[22]Podlubny, I.: Fractional differential equations, Math. sci. Eng. 198 (1999) · Zbl 0924.34008
[23]Prüss, J.: Evolutionary integral equations and applications, (1993)
[24]Scalas, E.; Gorenflo, R.; Mainardi, F.: Fractional calculus and continuous-time finance, Phys. A 284, 376-384 (2000)
[25]Yosida, K.: Fractional powers of infinitesimal generators and the analyticity of the semigroups generated by them, Proc. Japan acad. 36, 86-89 (1960) · Zbl 0097.31801 · doi:10.3792/pja/1195524080
[26]Zaslavsky, G. M.: Fractional kinetic equations for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion, Phys. D 76, 110-122 (1994) · Zbl 1194.37163 · doi:10.1016/0167-2789(94)90254-2
[27]Zwart, H.: Is A-1 an infinitesimal generator?, Banach center publ. 75, 303-313 (2007) · Zbl 1126.47039 · doi:http://journals.impan.gov.pl/bc/Cont/bc75-0.html