Research

 Publications A. Himonas, On analytic microlocal hypoellipticity of linear partial differential operators of principal type. Comm. Partial Differential Equations 11 (1986), no. 14, 1539--1574. A. Himonas, Semirigid partial differential operators and microlocal analytic hypoellipticity. Duke Math. J. 59 (1989), no. 1, 265--287. A. Himonas, On certain partial differential operators of finite odd type. Trans. Amer. Math. Soc. 324 (1991), no. 2, 889--900. A. Himonas, Finite type analytic partial differential operators and analytic hypoellipticity. Several complex variables and complex geometry, Part 3 (Santa Cruz, CA, 1989), 199--205, Proc. Sympos. Pure Math., 52, Part 3, Amer. Math. Soc., Providence, RI, 1991. N. Hanges and A. Himonas, Singular solutions for sums of squares of vector fields. Comm. Partial Differential Equations 16 (1991), no. 8-9, 1503--1511. A. Himonas, On hypoellipticity for sums of squares of vector fields. The Madison Symposium on Complex Analysis (Madison, WI, 1991), 267--275, Contemp. Math., 137, Amer. Math. Soc., Providence, RI, 1992. N. Hanges and A. Himonas, Analytic hypoellipticity for generalized Baouendi-Goulaouic operators. J. Funct. Anal. 125 (1994), no. 1, No. 07, 309--325. P. Cordaro and A. Himonas, Global analytic hypoellipticity of a class of degenerate elliptic operators on the torus. Math. Res. Lett. 1 (1994), no. 4, 501--510. A. Himonas, On degenerate elliptic operators of infinite type. Math. Z. 220 (1995), no. 3, 449--460. N. Hanges and A. Himonas, Singular solutions for a class of Grusin type operators. Proc. Amer. Math. Soc. 124 (1996), no. 5, 1549--1557. N. Hanges and A. Himonas, Non-analytic hypoellipticity in the presence of symplecticity. Proc. Amer. Math. Soc. 126 (1998), no. 2, 405--409. P. Cordaro and A. Himonas, Global analytic regularity for sums of squares of vector fields. Trans. Amer. Math. Soc. 350 (1998), no. 12, 4993--5001. A. Himonas and G. Petronilho, Global hypoellipticity for sums of squares of vector fields of infinite type. Fifth Workshop on Partial Differential Equations (Rio de Janeiro, 1997). Mat. Contemp. 15 (1998), 145--155.  A. Himonas, Analytic hypoellipticity for sums of squares of vector fields. Complex analysis and applications (Warsaw, 1997). Ann. Polon. Math. 70 (1998), 117--129. A. Himonas and G. Misiolek, The Cauchy problem for a shallow water type equation. Comm. Partial Differential Equations 23 (1998), no. 1-2, 123--139.  A. Himonas and G. Petronilho, On global hypoellipticity of degenerate elliptic operators. Math. Z. 230 (1999), no. 2, 241--257.  A. Himonas and G. Petronilho, Global hypoellipticiy and simultaneous approximability. J. Func. Anal. 170 , (2000), 356--365. A. Himonas and G. Misiolek, Global well-posedness of the Cauchy problem for a shallow waterequation on the circle. J. of Diff. Eq. 161, (2000), 479--495. A. Himonas and G. Misiolek, The initial value problem for a fifth order shallow water equation on the real line. Amer. Math. Soc., Analysis, geometry, number theory: the mathematics of Leon Ehrenpreis 251, (2000), 309--320. A. Himonas and G. Petronilho, Global hypoellipticity for sublaplacians. VI Workshop on Partial Differential Equations, Part I (Rio de Janeiro, 1999). Mat. Contemp. 18 (2000), 167--174. A. Himonas, Global analytic and Gevrey hypoellipticity of sublaplacians under diophantine conditions. Proc. Amer. Math. Soc. 129, No. 7, (2000), 2061--2067. A. Himonas and G. Misiolek, The Cauchy problem for an integrable shallow water equation. Differential Integral Equations 14, (2001), 821--831. A. Himonas and G. Misiolek, An a'priori estimate for Schrodinger type multipliers. Illinois J. Math. 45, (2001), 631--640. A. Himonas and G. Misiolek, A'priori estimates for higher order multipliers on a circle. Proc. Amer. Math. Soc. 130, (2002), 3043--3050. A. Himonas and G. Misiolek, Remarks on an integrable evolution equation. Geometry and analysis on finite- and infinite-dimensional Lie groups (Bedlewo, 2000), 77--85, Banach Center Publ., 55, Polish Acad. Sci., Warsaw, 2002. A. Himonas and G. Petronilho, Propagation of regularity and global hypoellipticity. Michigan Math. J. 50, (2002), 471--481. A. Himonas and G. Misiolek, Analyticity of the Cauchy problem for an integrable evolution equation. Math. Ann. 327, no. 3, (2003), 575--584. P. Byers and A. Himonas, Non-analytic solutions of the KdV equation. Abstr. Appl. Anal. 2004:6, (2004), 453--460. A. Himonas and G. Petronilho, On Gevrey regularity of globally $C^\infty$ hypoelliptic operators. J. Differential Equations 207 (2004), no. 2, 267--284.  J. Gorsky and A. Himonas, Construction of non-analytic solutions for the generalized KdV equation. J. Math. Anal. Appl. 303, (2005), no. 2, 522--529. J. Gorsky and A. Himonas, On analyticity in space variable of solutions to the KdV equation. Geometric analysis of PDE and several complex variables, Contemp. Math. 368, Amer. Math. Soc., (2005), 233--247. O. Calin, Y. Chen, T. Cosimano, and A. Himonas, Solving asset pricing models when the price-dividend function is analytic. Econometrica 73 (2005), no. 3, 961--982. A. Himonas and G. Misiolek, High-frequency smooth solutions and well-posedness of the Camassa-Holm equation. Int. Math. Res. Not. 2005, no. 51, 3135--3151. H. Hannah, A. Himonas and G. Petronilho, Gevrey regularity in time for generalized KdV type equations. Recent progress on some problems in several complex variables and partial differential equations, 117--127, Contemp. Math., 400, Amer. Math. Soc., Providence, RI, 2006. A. Himonas and G. Petronilho, On $C^\infty$ and Gevrey Regularity of Sublaplacians. Trans. Amer. Math. Soc. 358 (2006), no. 11, 4809--4820. A. Himonas, G. Petronilho and A. dos Santos, Regularity of a class of sublaplacians on the 3-dimensional torus. J. Funct. Anal. To appear. A. Himonas, G. Misiolek, G. Ponce and Y. Zhou, Persistence Properties and Unique Continuation of solutions of the Camassa-Holm equation. Comm. Math. Phys. 271, (2007), 511--522.