Journal Articles

Garetto, C (Accepted for publication) On the wave equation with multiplicities and space-dependent irregular coefficients, Transactions of the American Mathematical Society, ISSN: 0002-9947.

Garetto, C, Jäh, C, Ruzhansky, M (Accepted for publication) Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysis, Journal of Differential Equations, ISSN: 0022-0396.

Garetto, C, Jah, C, Ruzhansky, M (2018) Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness, Mathematische Annalen, 372(3-4), pp.1597-1629, ISSN: 0025-5831. DOI: 10.1007/s00208-018-1672-1.

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 Jaeh, C (2016) Well-posedness of hyperbolic systems with multiplicities and smooth coefficients, Mathematische Annalen, 369(1-2), pp.441-485, ISSN: 0025-5831. DOI: 10.1007/s00208-016-1436-8.

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) 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 (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 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 (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 (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, 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 (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 (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 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 (2005) Topological structures in Colombeau algebras: Investigation of the duals of script G sign c (Ω), script G sign(Ω) and script G sign script S sign (ℝ 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 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 (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.

Garetto, C (Accepted for publication) Generalized Fourier Integral Operators on spaces of Colombeau type.

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

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

Garetto, C and Ruzhansky, M (Accepted for publication) On weakly hyperbolic equations with analytic principal part, J. Math. Anal. Appl, 412 (2014), 1-14, DOI: 10.1016/j.jmaa.2013.09.011.

Garetto, C and Ruzhansky, M (Accepted for publication) Hyperbolic second order equations with non-regular time dependent coefficients, Arch. Ration. Mech. Anal, 217 (2015), 113-154, DOI: 10.1007/s00205-014-0830-1.

Garetto, C and Ruzhansky, M (Accepted for publication) On hyperbolic systems with time dependent Hölder characteristics.