Belluzi, Maykel; Bezerra, Flank D. M.; Nascimento, Marcelo J. D. On spectral and fractional powers of damped wave equations. (English) Zbl 1500.35293 Commun. Pure Appl. Anal. 21, No. 8, 2739-2773 (2022). MSC: 35R11 35L20 35J25 35P05 26A33 34A08 PDF BibTeX XML Cite \textit{M. Belluzi} et al., Commun. Pure Appl. Anal. 21, No. 8, 2739--2773 (2022; Zbl 1500.35293) Full Text: DOI OpenURL
Dinh, Huy; Antil, Harbir; Chen, Yanlai; Cherkaev, Elena; Narayan, Akil Model reduction for fractional elliptic problems using Kato’s formula. (English) Zbl 1486.35421 Math. Control Relat. Fields 12, No. 1, 115-146 (2022). MSC: 35R11 35J25 65M12 PDF BibTeX XML Cite \textit{H. Dinh} et al., Math. Control Relat. Fields 12, No. 1, 115--146 (2022; Zbl 1486.35421) Full Text: DOI arXiv OpenURL
Cholewa, Jan W.; Rodriguez-Bernal, Anibal Sharp estimates for homogeneous semigroups in homogeneous spaces. Applications to PDEs and fractional diffusion in \(\mathbb{R}^N\). (English) Zbl 1497.47058 Commun. Contemp. Math. 24, No. 1, Article ID 2050070, 56 p. (2022). MSC: 47D03 47D06 35K10 35K25 35R11 35Q35 35Q40 PDF BibTeX XML Cite \textit{J. W. Cholewa} and \textit{A. Rodriguez-Bernal}, Commun. Contemp. Math. 24, No. 1, Article ID 2050070, 56 p. (2022; Zbl 1497.47058) Full Text: DOI OpenURL
Belluzi, Maykel; Nascimento, Marcelo J. D.; Schiabel, Karina On a cascade system of Schrödinger equations. Fractional powers approach. (English) Zbl 1479.35709 J. Math. Anal. Appl. 506, No. 1, Article ID 125644, 23 p. (2022). MSC: 35Q41 35K52 26A33 35R11 PDF BibTeX XML Cite \textit{M. Belluzi} et al., J. Math. Anal. Appl. 506, No. 1, Article ID 125644, 23 p. (2022; Zbl 1479.35709) Full Text: DOI OpenURL
Bezerra, Flank D. M.; Figueroa-López, Rodiak N.; Nascimento, Marcelo J. D. Fractional oscillon equations; solvability and connection with classical oscillon equations. (English) Zbl 1483.35024 Commun. Pure Appl. Anal. 20, No. 6, 2257-2277 (2021). MSC: 35B40 35B41 34A08 35L20 35L71 35R11 47D06 PDF BibTeX XML Cite \textit{F. D. M. Bezerra} et al., Commun. Pure Appl. Anal. 20, No. 6, 2257--2277 (2021; Zbl 1483.35024) Full Text: DOI arXiv OpenURL
Kleiner, T.; Hilfer, R. Fractional glassy relaxation and convolution modules of distributions. (English) Zbl 1483.46038 Anal. Math. Phys. 11, No. 3, Paper No. 130, 29 p. (2021). MSC: 46F10 46F12 44A35 34A08 46N20 26A33 PDF BibTeX XML Cite \textit{T. Kleiner} and \textit{R. Hilfer}, Anal. Math. Phys. 11, No. 3, Paper No. 130, 29 p. (2021; Zbl 1483.46038) Full Text: DOI OpenURL
Antil, Harbir; Drăgănescu, Andrei; Green, Kiefer A note on multigrid preconditioning for fractional PDE-constrained optimization problems. (English) Zbl 1486.65278 Results Appl. Math. 9, Article ID 100133, 10 p. (2021). MSC: 65N55 26A33 35R11 49M41 PDF BibTeX XML Cite \textit{H. Antil} et al., Results Appl. Math. 9, Article ID 100133, 10 p. (2021; Zbl 1486.65278) Full Text: DOI arXiv OpenURL
Glusa, Christian; Antil, Harbir; D’Elia, Marta; van Bloemen Waanders, Bart; Weiss, Chester J. A fast solver for the fractional Helmholtz equation. (English) Zbl 1471.65208 SIAM J. Sci. Comput. 43, No. 2, A1362-A1388 (2021). MSC: 65N35 65N30 65N12 65N15 65N22 35J05 35A01 35A02 35B65 35R11 PDF BibTeX XML Cite \textit{C. Glusa} et al., SIAM J. Sci. Comput. 43, No. 2, A1362--A1388 (2021; Zbl 1471.65208) Full Text: DOI OpenURL
Bezerra, Flank D. M.; Carvalho, Alexandre N.; Nascimento, Marcelo J. D. Fractional approximations of abstract semilinear parabolic problems. (English) Zbl 1452.35085 Discrete Contin. Dyn. Syst., Ser. B 25, No. 11, 4221-4255 (2020). MSC: 35K90 35K58 35B41 47D06 PDF BibTeX XML Cite \textit{F. D. M. Bezerra} et al., Discrete Contin. Dyn. Syst., Ser. B 25, No. 11, 4221--4255 (2020; Zbl 1452.35085) Full Text: DOI OpenURL
Meichsner, Jan; Seifert, Christian On the harmonic extension approach to fractional powers in Banach spaces. (English) Zbl 1474.47055 Fract. Calc. Appl. Anal. 23, No. 4, 1054-1089 (2020). MSC: 47B12 47D06 47A60 PDF BibTeX XML Cite \textit{J. Meichsner} and \textit{C. Seifert}, Fract. Calc. Appl. Anal. 23, No. 4, 1054--1089 (2020; Zbl 1474.47055) Full Text: DOI arXiv OpenURL
Bezerra, Flank D. M.; Santos, Lucas A. Fractional powers approach of operators for abstract evolution equations of third order in time. (English) Zbl 1468.34091 J. Differ. Equations 269, No. 7, 5661-5679 (2020). Reviewer: Hristo S. Kiskinov (Plovdiv) MSC: 34G10 47D06 47D03 PDF BibTeX XML Cite \textit{F. D. M. Bezerra} and \textit{L. A. Santos}, J. Differ. Equations 269, No. 7, 5661--5679 (2020; Zbl 1468.34091) Full Text: DOI OpenURL
Idriss, Ali Zakaria; Razafimandimby, Paul André Stochastic generalized magnetohydrodynamics equations with not regular multiplicative noise: well-posedness and invariant measure. (English) Zbl 1478.60186 J. Math. Anal. Appl. 474, No. 2, 1404-1440 (2019). MSC: 60H15 76W05 35Q35 35Q30 35R60 PDF BibTeX XML Cite \textit{A. Z. Idriss} and \textit{P. A. Razafimandimby}, J. Math. Anal. Appl. 474, No. 2, 1404--1440 (2019; Zbl 1478.60186) Full Text: DOI OpenURL
Colombo, Fabrizio; Gantner, Jonathan An application of the \(S\)-functional calculus to fractional diffusion processes. (English) Zbl 1447.47063 Milan J. Math. 86, No. 2, 225-303 (2018). MSC: 47S05 47A60 47A10 26A33 60J60 47N20 PDF BibTeX XML Cite \textit{F. Colombo} and \textit{J. Gantner}, Milan J. Math. 86, No. 2, 225--303 (2018; Zbl 1447.47063) Full Text: DOI arXiv OpenURL
Colombo, Fabrizio; Gantner, Jonathan Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space. (English) Zbl 1401.60151 J. Phys. A, Math. Theor. 51, No. 30, Article ID 305201, 25 p. (2018). MSC: 60J60 60G22 80A20 PDF BibTeX XML Cite \textit{F. Colombo} and \textit{J. Gantner}, J. Phys. A, Math. Theor. 51, No. 30, Article ID 305201, 25 p. (2018; Zbl 1401.60151) Full Text: DOI arXiv OpenURL
Slade, Gordon Critical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimension. (English) Zbl 1391.82022 Commun. Math. Phys. 358, No. 1, 343-436 (2018). Reviewer: Hasan Akin (Gaziantep) MSC: 82B27 82B20 82B41 82B28 PDF BibTeX XML Cite \textit{G. Slade}, Commun. Math. Phys. 358, No. 1, 343--436 (2018; Zbl 1391.82022) Full Text: DOI arXiv OpenURL
Colombo, Fabrizio; Gantner, Jonathan Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity. (English) Zbl 06814519 Trans. Am. Math. Soc. 370, No. 2, 1045-1100 (2018). MSC: 47A10 47A60 PDF BibTeX XML Cite \textit{F. Colombo} and \textit{J. Gantner}, Trans. Am. Math. Soc. 370, No. 2, 1045--1100 (2018; Zbl 06814519) Full Text: DOI arXiv OpenURL
Colombo, Fabrizio; Gantner, Jonathan An introduction to fractional powers of quaternionic operators and new fractional diffusion processes. (English) Zbl 06864061 Colombo, Fabrizio (ed.) et al., Advances in complex analysis and operator theory. Festschrift in honor of Daniel Alpay’s 60th birthday. Contributions partly based on the presentations at the international conference on complex analysis and operator theory, Chapman University, Orange, CA, USA, November 2016. Cham: Birkhäuser/Springer. Trends Math., 101-134 (2017). MSC: 47-XX 47A10 47A60 PDF BibTeX XML Cite \textit{F. Colombo} and \textit{J. Gantner}, in: Advances in complex analysis and operator theory. Festschrift in honor of Daniel Alpay's 60th birthday. Contributions partly based on the presentations at the international conference on complex analysis and operator theory, Chapman University, Orange, CA, USA, November 2016. Cham: Birkhäuser/Springer. 101--134 (2017; Zbl 06864061) Full Text: DOI OpenURL
Cholewa, Jan W.; Quesada, Carlos; Rodríguez-Bernal, Aníbal Nonlinear evolution equations in scales of Banach spaces and applications to PDEs. (English) Zbl 1390.35174 J. Abstr. Differ. Equ. Appl. 8, No. 2, 1-69 (2017). MSC: 35K90 35B33 35K58 35K25 PDF BibTeX XML Cite \textit{J. W. Cholewa} et al., J. Abstr. Differ. Equ. Appl. 8, No. 2, 1--69 (2017; Zbl 1390.35174) Full Text: Link OpenURL
Bezerra, F. D. M.; Carvalho, A. N.; Cholewa, J. W.; Nascimento, M. J. D. Parabolic approximation of damped wave equations via fractional powers: fast growing nonlinearities and continuity of the dynamics. (English) Zbl 1356.35141 J. Math. Anal. Appl. 450, No. 1, 377-405 (2017). MSC: 35L71 35R11 35B40 35B41 PDF BibTeX XML Cite \textit{F. D. M. Bezerra} et al., J. Math. Anal. Appl. 450, No. 1, 377--405 (2017; Zbl 1356.35141) Full Text: DOI OpenURL
Batty, Charles; Gomilko, Alexander; Tomilov, Yuri Resolvent representations for functions of sectorial operators. (English) Zbl 1450.47011 Adv. Math. 308, 896-940 (2017). Reviewer: Khristo N. Boyadzhiev (Ada) MSC: 47B12 47A10 30C45 47D03 47A60 30E20 PDF BibTeX XML Cite \textit{C. Batty} et al., Adv. Math. 308, 896--940 (2017; Zbl 1450.47011) Full Text: DOI arXiv OpenURL
Chen, Chuang; Li, Miao Characterizations of domains of fractional powers for non-negative operators. (English) Zbl 1326.47001 J. Math. Anal. Appl. 435, No. 1, 179-209 (2016). MSC: 47A05 47A60 47D06 26A33 PDF BibTeX XML Cite \textit{C. Chen} and \textit{M. Li}, J. Math. Anal. Appl. 435, No. 1, 179--209 (2016; Zbl 1326.47001) Full Text: DOI OpenURL
Chen, Chuang; Kostić, Marko; Li, Miao Representation of complex powers of \(C\)-sectorial operators. (English) Zbl 1318.47056 Fract. Calc. Appl. Anal. 17, No. 3, 827-854 (2014). Reviewer: Rodica Luca (Iaşi) MSC: 47D06 47D60 47D62 PDF BibTeX XML Cite \textit{C. Chen} et al., Fract. Calc. Appl. Anal. 17, No. 3, 827--854 (2014; Zbl 1318.47056) Full Text: DOI OpenURL
Dungey, Nick Subordinated discrete semigroups of operators. (English) Zbl 1228.47012 Trans. Am. Math. Soc. 363, No. 4, 1721-1741 (2011). Reviewer: Wilfried Hazod (Dortmund) MSC: 47A30 60G50 47A60 47D06 PDF BibTeX XML Cite \textit{N. Dungey}, Trans. Am. Math. Soc. 363, No. 4, 1721--1741 (2011; Zbl 1228.47012) Full Text: DOI arXiv OpenURL
Li, Miao; Chen, Chuang; Li, Fu-Bo On fractional powers of generators of fractional resolvent families. (English) Zbl 1203.47021 J. Funct. Anal. 259, No. 10, 2702-2726 (2010). Reviewer: Vincenzo Vespri (Firenze) MSC: 47D06 35K90 47D60 PDF BibTeX XML Cite \textit{M. Li} et al., J. Funct. Anal. 259, No. 10, 2702--2726 (2010; Zbl 1203.47021) Full Text: DOI arXiv OpenURL
Dungey, Nick Asymptotic type for sectorial operators and an integral of fractional powers. (English) Zbl 1162.47032 J. Funct. Anal. 256, No. 5, 1387-1407 (2009). Reviewer: Birgit Jacob (Paderborn) MSC: 47B99 47D03 PDF BibTeX XML Cite \textit{N. Dungey}, J. Funct. Anal. 256, No. 5, 1387--1407 (2009; Zbl 1162.47032) Full Text: DOI OpenURL
Carvalho, A. N.; Cholewa, J. W.; Dlotko, Tomasz Strongly damped wave problems: bootstrapping and regularity of solutions. (English) Zbl 1151.35056 J. Differ. Equations 244, No. 9, 2310-2333 (2008). Reviewer: Marie Kopáčková (Praha) MSC: 35L70 35B33 35B65 PDF BibTeX XML Cite \textit{A. N. Carvalho} et al., J. Differ. Equations 244, No. 9, 2310--2333 (2008; Zbl 1151.35056) Full Text: DOI OpenURL
Krägeloh, Alexander M. Two families of functions related to the fractional powers of generators of strongly continuous contraction semigroups. (English) Zbl 1061.47038 J. Math. Anal. Appl. 283, No. 2, 459-467 (2003). Reviewer: Pedro José Miana (Zaragoza) MSC: 47D06 44A10 PDF BibTeX XML Cite \textit{A. M. Krägeloh}, J. Math. Anal. Appl. 283, No. 2, 459--467 (2003; Zbl 1061.47038) Full Text: DOI OpenURL
deLaubenfels, Ralph Similarity to a contraction, for power-bounded operators with finite peripheral spectrum. (English) Zbl 0899.47012 Trans. Am. Math. Soc. 350, No. 8, 3169-3191 (1998). MSC: 47A65 47A60 47D03 47A45 47A10 47A12 47A05 PDF BibTeX XML Cite \textit{R. deLaubenfels}, Trans. Am. Math. Soc. 350, No. 8, 3169--3191 (1998; Zbl 0899.47012) Full Text: DOI OpenURL
Karakas, H. I.; Shakhmurov, V. B.; Yakubov, S. Degenerate elliptic boundary value problems. (English) Zbl 0872.34038 Appl. Anal. 60, No. 1-2, 155-174 (1996). Reviewer: H.I.Karakas (Haifa) MSC: 34G10 35J25 35J70 PDF BibTeX XML Cite \textit{H. I. Karakas} et al., Appl. Anal. 60, No. 1--2, 155--174 (1996; Zbl 0872.34038) Full Text: DOI OpenURL
Pereira, Antônio L. Eigenvalues of the Laplacian on symmetric regions. (English) Zbl 0824.35091 NoDEA, Nonlinear Differ. Equ. Appl. 2, No. 1, 63-109 (1995). Reviewer: R.Sperb (Zürich) MSC: 35P20 35J05 PDF BibTeX XML Cite \textit{A. L. Pereira}, NoDEA, Nonlinear Differ. Equ. Appl. 2, No. 1, 63--109 (1995; Zbl 0824.35091) Full Text: DOI OpenURL
Fujita, Yasuhiro Holomorphic resolvent for integrodifferential equation with completely positive measure. (English) Zbl 0808.45017 Math. Ann. 300, No. 1, 29-40 (1994). Reviewer: O.Staffans (Espoo) MSC: 45N05 47D03 PDF BibTeX XML Cite \textit{Y. Fujita}, Math. Ann. 300, No. 1, 29--40 (1994; Zbl 0808.45017) Full Text: DOI EuDML OpenURL
Martínez, Celso; Sanz, Miguel Fractional powers of non-densely defined operators. (English) Zbl 0811.47013 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 18, No. 3, 443-454 (1991). Reviewer: A.Torgašev (Beograd) MSC: 47A60 47A05 PDF BibTeX XML Cite \textit{C. Martínez} and \textit{M. Sanz}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 18, No. 3, 443--454 (1991; Zbl 0811.47013) Full Text: Numdam EuDML OpenURL
Martínez, Celso; Sanz, Miguel n-th roots of a non-negative operator. Conditions for uniqueness. (English) Zbl 0684.47014 Manuscr. Math. 64, No. 4, 403-417 (1989). Reviewer: A.Torgašev MSC: 47A60 47B15 PDF BibTeX XML Cite \textit{C. Martínez} and \textit{M. Sanz}, Manuscr. Math. 64, No. 4, 403--417 (1989; Zbl 0684.47014) Full Text: DOI EuDML OpenURL
Guzman, Alberto Growth properties of semigroups generated by fractional powers of certain linear operators. (English) Zbl 0342.47022 J. Funct. Anal. 23, 331-352 (1976). MSC: 47D03 PDF BibTeX XML Cite \textit{A. Guzman}, J. Funct. Anal. 23, 331--352 (1976; Zbl 0342.47022) Full Text: DOI OpenURL
Ichinose, T. Operators on tensor products of Banach spaces. (English) Zbl 0215.48902 Trans. Am. Math. Soc. 170, 197-219 (1972). MSC: 47B99 46M05 47A20 PDF BibTeX XML Cite \textit{T. Ichinose}, Trans. Am. Math. Soc. 170, 197--219 (1972; Zbl 0215.48902) Full Text: DOI OpenURL
Cooper, J. M. Two-point problems for abstract evolution equations. (English) Zbl 0219.35016 J. Differ. Equations 9, 453-495 (1971). MSC: 35F15 35G10 35K25 PDF BibTeX XML Cite \textit{J. M. Cooper}, J. Differ. Equations 9, 453--495 (1971; Zbl 0219.35016) Full Text: DOI OpenURL
Lagnese, John E. On equations of evolution and parabolic equations of higher order in t. (English) Zbl 0207.14002 J. Math. Anal. Appl. 32, 15-37 (1970). MSC: 47D06 47D03 47A20 47F05 47A10 PDF BibTeX XML Cite \textit{J. E. Lagnese}, J. Math. Anal. Appl. 32, 15--37 (1970; Zbl 0207.14002) Full Text: DOI OpenURL
Westphal, U. Ein Kalkül für gebrochene Potenzen infinitesimaler Erzeuger von Halbgruppen und Gruppen von Operatoren. I: Halbgruppenerzeuger. (German) Zbl 0194.15401 Compos. Math. 22, 67-103 (1970). PDF BibTeX XML Cite \textit{U. Westphal}, Compos. Math. 22, 67--103 (1970; Zbl 0194.15401) Full Text: Numdam EuDML OpenURL
Burak, Tamar Fractional powers of elliptic differential operators. (English) Zbl 0159.15601 Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 22, 113-132 (1968). Reviewer: Yu. V. Egorov MSC: 35Jxx PDF BibTeX XML Cite \textit{T. Burak}, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 22, 113--132 (1968; Zbl 0159.15601) Full Text: Numdam EuDML OpenURL
Schechter, M. Complex interpolation. (English) Zbl 0153.16402 Compos. Math. 18, 117-147 (1967). PDF BibTeX XML Cite \textit{M. Schechter}, Compos. Math. 18, 117--147 (1967; Zbl 0153.16402) Full Text: Numdam EuDML OpenURL
Schechter, M. Interpolation spaces by complex methods. (English) Zbl 0197.38901 Bull. Am. Math. Soc. 72, 526-533 (1966). PDF BibTeX XML Cite \textit{M. Schechter}, Bull. Am. Math. Soc. 72, 526--533 (1966; Zbl 0197.38901) Full Text: DOI OpenURL
Miyadera, Isao A perturbation theorem for contraction semi-groups. (English) Zbl 0148.38503 Proc. Japan Acad. 42, 755-758 (1966). PDF BibTeX XML Cite \textit{I. Miyadera}, Proc. Japan Acad. 42, 755--758 (1966; Zbl 0148.38503) Full Text: DOI OpenURL
Asano, K. On semi-linear parabolic partial differential equations. (English) Zbl 0192.19801 Publ. Res. Inst. Math. Sci., Kyoto Univ., Ser. A 1, 67-98 (1965). PDF BibTeX XML Cite \textit{K. Asano}, Publ. Res. Inst. Math. Sci., Ser. A 1, 67--98 (1965; Zbl 0192.19801) Full Text: DOI OpenURL
Kato, T. Abstract evolution equations of parabolic type in Banach and Hilbert spaces. (English) Zbl 0114.06102 Nagoya Math. J. 19, 93-125 (1961). PDF BibTeX XML Cite \textit{T. Kato}, Nagoya Math. J. 19, 93--125 (1961; Zbl 0114.06102) Full Text: DOI OpenURL