# Publications for Claudia Garetto

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## Journal Articles

**Garetto, C**and Ruzhansky, M (2017) On C∞ well-posedness of hyperbolic systems with multiplicities,

*Annali di Matematica Pura ed Applicata*, ISSN: 1618-1891. DOI: 10.1007/s10231-017-0639-2.

**Garetto, C**and Jäh, C (2016) Well-posedness of hyperbolic systems with multiplicities and smooth coefficients,

*Mathematische Annalen*, pp.1-45, ISSN: 0025-5831. DOI: 10.1007/s00208-016-1436-8.

**Garetto, C**and Ruzhansky, M (2016) On hyperbolic systems with time dependent Hölder characteristics.

**Garetto, C**(2015) On hyperbolic equations and systems with non-regular time dependent coefficients,

*Journal of Differential Equations*, In press(In press), ISSN: 1090-2732. DOI: 10.1016/j.jde.2015.07.011.

**Garetto, C**and Ruzhansky, M (2015) Wave equation for sums of squares on compact Lie groups,

*Journal of Differential Equations*, 258(12), pp.4324-4347, ISSN: 0022-0396. DOI: 10.1016/j.jde.2015.01.034.

**Garetto, C**and Ruzhansky, M (2013) Hyperbolic second order equations with non-regular time dependent coefficients,

*Arch. Ration. Mech. Anal, 217 (2015), 113-154*, Full text: http://dx.doi.org/10.1007/s00205-014-0830-1. DOI: 10.1007/s00205-014-0830-1.

**Garetto, C**and Ruzhansky, M (2013) On weakly hyperbolic equations with analytic principal part,

*J. Math. Anal. Appl, 412 (2014), 1-14*, Full text: http://dx.doi.org/10.1016/j.jmaa.2013.09.011. DOI: 10.1016/j.jmaa.2013.09.011.

**Garetto, C**and Ruzhansky, M (2013) Weakly hyperbolic equations with non-analytic coefficients and lower order terms,

*Mathematische Annalen*, 357(2), pp.401-440, ISSN: 0025-5831. DOI: 10.1007/s00208-013-0910-9.

**Garetto, C**and Ruzhansky, M (2012) On the well-posedness of weakly hyperbolic equations with time-dependent coefficients,

*Journal of Differential Equations*, 253(5), pp.1317-1340, ISSN: 0022-0396. DOI: 10.1016/j.jde.2012.05.001.

**Garetto, C**and Oberguggenberger, M (2011) Generalised Fourier integral operator methods for hyperbolic equations with singularities.

**Garetto, C**and Oberguggenberger, M (2011) Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients.

**Garetto, C**and Vernaeve, H (2011) Hilbert ℂ̃-modules: Structural properties and applications to variational problems,

*Transactions of the American Mathematical Society*, 363(4), pp.2047-2090, ISSN: 0002-9947. DOI: 10.1090/S0002-9947-2010-05143-8.

**Garetto, C**(2011) Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach,

*Journal of Mathematical Analysis and Applications*, 381(1), pp.328-343, ISSN: 0022-247X. DOI: 10.1016/j.jmaa.2011.02.056.

**Garetto, C**(2010) G- and G∞-hypoellipticity of partial differential operators with constant Colombeau coefficients,

*Banach Center Publications*, 88, pp.111-131.

**Garetto, C**(2009) Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type,

*Electronic Journal of Differential Equations*, 2009, pp.1-43.

**Garetto, C**, Hörmann, G, Oberguggenberger, M (2009) Generalized oscillatory integrals and fourier integral operators,

*Proceedings of the Edinburgh Mathematical Society*, 52(2), pp.351-386, ISSN: 0013-0915. DOI: 10.1017/S0013091506000915.

**Garetto, C**(2009) Closed graph and open mapping theorems for topological ℂ̃-modules and applications,

*Mathematische Nachrichten*, 282(8), pp.1159-1188, ISSN: 0025-584X. DOI: 10.1002/mana.200610793.

**Garetto, C**(2008) Generalized Fourier Integral Operators on spaces of Colombeau type.

**Garetto, C**(2008) Fundamental solutions in the colombeau framework: Applications to solvability and regularity theory,

*Acta Applicandae Mathematicae*, 102(2-3), pp.281-318, ISSN: 0167-8019. DOI: 10.1007/s10440-008-9220-8.

**Garetto, C**and Hoermann, G (2006) On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave fron sets,

*Academie Serbe des Sciences et des Arts, Classe des Sciences Mathematiques et Naturelles: Bulletin S*, 31, pp.115-136.

**Garetto, C**(2006) Microlocal analysis in the dual of a Colombeau algebra: Generalized wave front sets and noncharacteristic regularity,

*New York Journal of Mathematics*, 12, pp.275-318, ISSN: 1076-9803.

**Garetto, C**and Hörmann, G (2005) Microlocal analysis of generalized functions: Pseudodifferential techniques and propagation of singularities,

*Proceedings of the Edinburgh Mathematical Society*, 48(3), pp.603-629, ISSN: 0013-0915. DOI: 10.1017/S0013091504000148.

**Garetto, C**(2005) Topological structures in Colombeau algebras: Topological ℂ̃-modules and duality theory,

*Acta Applicandae Mathematicae*, 88(1), pp.81-123, ISSN: 0167-8019. DOI: 10.1007/s10440-005-6700-y.

**Garetto, C**(2005) Topological structures in Colombeau algebras: Investigation of the duals of script G sign

^{n}),

*Monatshefte fur Mathematik*, 146(3), pp.203-226, ISSN: 0026-9255. DOI: 10.1007/s00605-005-0331-2.

**Garetto, C**, Gramchev, T, Oberguggenberger, M (2005) Pseudodifferential operators with generalized symbols and regularity theory,

*Electronic Journal of Differential Equations*, 2005, ISSN: 1072-6691.

**Garetto, C**(2004) Pseudo-differential operators in algebras of generalized functions and global hypoellipticity,

*Acta Applicandae Mathematicae*, 80(2), pp.123-174, ISSN: 0167-8019. DOI: 10.1023/B:ACAP.0000013814.89972.3c.

## Other

**Garetto, C**, Jäh, C, Ruzhansky, M (Accepted for publication)

*Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness*, © 2018 The Author(s) In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a well-posedness result in anisotropic Sobolev spaces for systems with upper triangular principal part under interesting natural conditions on the orders of lower order terms below the diagonal. Namely, the terms below the diagonal at a distance k to it must be of order (Formula presented.). This setting also allows for the Jordan block structure in the system. Second, we give conditions for the Schur type triangularisation of general systems with variable coefficients for reducing them to the form with an upper triangular principal part for which the first result can be applied. We give explicit details for the appearing conditions and constructions for (Formula presented.) and (Formula presented.) systems, complemented by several examples. DOI: 10.1007/s00208-018-1672-1.