uniform approximation of holomorphic functions on bounded hartogs domains in ℂ2 on etudie l algebre a des fonctions continues sur qui sont holomorphes dans approximation uniforme des fonctions de a par des fonctions holomorphes dans un voisinage de question de la densite uniforme dans a de l algebre a des fonctions regulieres sur qui sont holomorphes dans

an ambrosetti prodi type result for doubly periodic solutions of the telegraph system abstract this article deals with an ambrosetti prodi type result for doubly periodic solutions of the telegraph system by using leray schauder degree theory the method of upper and lower solutions

regularity of the bergman projection on forms and plurisubharmonicity conditions let omega subset subset mathbb c n be a smoothly bounded domain suppose has a defining function such that the sum of any q eigenvalues of its complex hessian is non negative we show that this implies global regularity of the bergman projection b j 1 and the bar partial neumann operator n j acting on 0 j forms for j in q ldots n

the cauchy szegő projection for domains in mathbb c n with minimal smoothness we prove the lp bd regularity of the cauchy szeg projection also known as the szeg projection for bounded domains d cn which are strongly pseudoconvex and whose boundary satisfies the minimal regularity condition of class c2

an ambrosetti prodi type result for periodic solutions of the telegraph equation using leray schander degree theory a theorem of upper and lower solutions and a strong maximum principle for the telegraph equation we prove an ambrosetti prodi type result for periodic solutions of the telegraph equation

behavior of the bergman projection on the diederich fornaess worm w 1 introduction in this paper we show that the bergman projection operator for certain smooth bounded pseudoconvex domains does not preserve smoothness as measured by sobolev norms let q be a smooth bounded pseudoconvex domain in c and let p t denote the orthogonal projection from l2 f onto the bergman subspace b ff l2 f3 r with respect to the weighted norm i fll j olf z l 2 e t lzll2dv l 2 let wk t denote the sobolev space consisting of functions whose derivatives of order to k g2 on the other hand there is a large collection of results implying that for certain types of domains the unweighted bergman projection p pr preserves w k for all k 0 see fk for the strictly pseudoconvex case for results on weakly pseudoconvex domains the reader may consult ko2 ca si and the recent bstl ch as well as the references cited therein most of these results are focused on the a neumann operator rather than p see bst2 for the connection also except for kol positive results in this area are typically valid for any choice of smooth positive weight function on 0 the question of whether or not p is similarly well behaved for all weakly pseudoconvex domains has remained open for many years in this paper we show that this is not the case in fact when q is the so called worm domain of diederich and forna ss then p does not map w to w k when k zr total amount of winding this latter quantity is explained in section 4 below where the construction of the worm is reviewed and the main result is proved the proof depends on computations for a piecewise levi flat model domain depending in turn on certain one dimensional computations these are treated in sections 3 and 2 respectively section 5 contains additional remarks and questions

existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system abstract in this paper the existence of positive doubly periodic solutions for nonlinear telegraph system is discussed using the method of upper and lower solutions

lp regularity of the bergman projection on domains covered by the polydisc abstract if a bounded domain can be covered by the polydisc through a rational proper holomorphic map then the bergman projection is l p bounded for p in a non trivial interval depending on the ramified rational covering this result can be applied to the symmetrized polydisc and to the hartogs triangle with exponent

a maximum principle for periodic solutions of the telegraph equation let l s l u be a linear differential operator acting on functions u v a r that are defined on a fixed manifold v these functions will belong to a certain family b f v r and the definition of b may include some boundary conditions or other requirements that must be satisfied by any function u g b it is said that l satisfies the maximum principle if the differential inequality l u g 0 u g b implies u g 0 in v w x the book 18 is devoted to the study of the maximum principle for second w x w x w x w x w x order operators other related results can be found in 17 5 12 8 2 w x 14 in this paper we study the maximum principle for periodic solutions of the telegraph equation the operator is

characterization of automorphisms on the barrett and the diederich fornaess worm domains in this paper we show that every automorphism on either the barrett or the diederick fornaess worm domains is given by a rotation in w variable in particular any automorphism on either one of these two domains can be extended smoothly up to the boundary

duality and approximation of bergman spaces abstract expected duality and approximation properties are shown to fail on bergman spaces of domains in c n via examples when the domain admits an operator satisfying certain mapping properties positive duality and approximation results are proved such operators are constructed on generalized hartogs triangles on a general bounded reinhardt domain norm convergence of laurent series of bergman functions is shown this extends a classical result on hardy spaces of the unit disc

positive doubly periodic solutions of nonlinear telegraph equations abstract this paper deals with the existence of nontrivial doubly periodic solutions for the nonlinear telegraph equation u tt u xx cu t a t x u b t x f t x u t x r 2 where c 0 is a constant a b c r 2 r f c r 2 r r and a b f are 2 periodic in t and x we show the existence of positive doubly periodic weak solutions when 0 a t x c2 4 and f is either superlinear or sublinear on u by using the krasnoselskii s fixed point theorem in cones

simultaneous control problems for systems of elastic strings and beams abstract controllability problems for n strings or beams controlled from a common endpoint are studied we give necessary and sufficient conditions for simultaneous spectral and approximate controllability and describe the space of simultaneously reachable states as a function of the position of the endpoint for each type of controllability result the sharp controllability time is obtained the proofs are based on new results in nonharmonic fourier series which describe riesz bases of exponential divided differences