a sufficient condition for compactness of the neumann operator we show that the existence of a certain family of plurisubharmonic functions on a bounded domain in cn implies that the neumann operator associated to the domain is compact our condition generalizes previous work of catlin on compactness of the neumann operator

the diederich fornaess index and the global regularity of the bar partial neumann problem we describe along the guidelines of kohn quantitative estimates for global regularity analysis and geometry in several complex variables pp 97 128 trend math birkhauser boston 1999 the constant mathcal e s which is needed to control the commutator of a totally real vector field t mathcal e with bar partial in order to have h s a priori estimates for the bergman projection b k k ge q 1 on a smooth q convex domain d subset subset mathbb c n this statement not explicit in kohn quantitative estimates for global regularity analysis and geometry in several complex variables pp 97 128 trend math birkhauser boston 1999 yields regularity of b k in specific sobolev degree s next we refine the pseudodifferential calculus at the boundary in order to relate for a defining function r of d the operators t frac delta 2 and r frac delta 2 we are thus able to extend to general degree k ge 0 of b k the conclusion of quantitative estimates for global regularity analysis and geometry in several complex variables pp 97 128 trend math birkhauser boston 1999 which only holds for q 1 and k 0 if for the diederich fornaess index delta of d we have 1 delta frac 1 2 le mathcal e s then b k is h s regular

hearing the type of a domain in c 2 with the neumann laplacian a smooth bounded pseudoconvex domain in c2 is of finite type if and only if the number of eigenvalues of its a neumann laplacian that are less than or equal to has at most polynomial growth as goes to infinity

stein compacts in levi flat hypersurfaces we explore connections between geometric properties of the levi foliation of a levi flat hypersurface m and holomorphic convexity of compact sets in m or bounded in part by m applications include extendability of cauchy riemann functions solvability of the b equation approximation of cauchy riemann and holomorphic functions and global regularity of the neumann operator

levi foliations in pseudoconvex boundaries and vector fields that commute approximately with boas and straube proved a general sufficient condition for global regularity of the neumann problem in terms of families of vector fields that commute approximately with in this paper we study the existence of these vector fields on a compact subset of the boundary whose interior is foliated by complex manifolds this question turns out to be closely related to properties of interest from the point of view of foliation theory

a sufficient condition for global regularity of the neumann operator abstract a theory of global regularity of the neumann operator is developed which unifies the two principal approaches to date namely the one via compactness due to kohn nirenberg j j kohn l nirenberg non coercive boundary value problems comm pure appl math 18 1965 443 492 and catlin david catlin global regularity of the neumann problem in y t siu ed complex analysis of several variables in proc sympos pure math vol 41 amer math soc providence ri 1984 pp 39 49 and the one via plurisubharmonic defining functions and or vector fields that commute approximately with due to boas and the author harold p boas emil j straube sobolev estimates for the neumann operator on domains in c n admitting a defining function that is plurisubharmonic on the boundary math z 206 1 1991 81 88 harold p boas emil j straube de rham cohomology of manifolds containing the points of infinite type and sobolev estimates for the neumann problem j geom anal 3 3 1993 225 235

superlogarithmic estimates on pseudoconvex domains and cr manifolds this paper is concerned with proving superlogarithmic estimates for the operator r b on pseudoconvex cr manifolds and using them to establish hypoellipticity of lb and of the neumann problem these estimates are established under the assumption that subellipticity degenerates in certain specified ways

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

a kleene theorem for weighted tree automata over tree valuation monoids abstract we investigate weighted tree automata over cauchy tree valuation monoids a new type of weight structure which includes all commutative semirings and in addition average and discounted computations of weights for trees we define rational tree series over these weight structures and we prove kleene s classical theorem for this setting a tree series over a cauchy tree valuation monoid is recognizable by a weighted tree automaton if and only if it is rational the proof works via direct automata theoretic constructions along the way our results yield a new characterization of weighted tree automata over commutative semirings by rational expressions

a link between multioperator and tree valuation automata and logics weighted tree languages over semirings lack the expressive power to model computations like taking the average or the discounting of weights in a straightforward manner this limitation was overcome by weighted tree automata and logics using a tree valuation monoids and b multioperator monoids we compare the expressive power of these two solutions and show that a weighted tree language recognizable resp definable over a tree valuation monoid is also recognizable resp definable using a multioperator monoid for this we provide direct semantic preserving transformations between the automata models and between the respective logics we research the relationship between two classes of weighted tree languages we give a construction from one automaton model to the other preserving the language an analogous result is shown for the corresponding weighted tree logics a direct transformation between the logics avoids nonelementary blow up

the bergman projection on hartogs domains in estimates in l 2 sobolev norms are proved for the bergman projection in certain smooth bounded hartogs domains in c 2 in particular 1 if the domain is pseudoconvex and nonwormlike the normal vector does not wind on a critical set in the boundary then the bergman projection is regular and 2 barrett s counter example domains with irregular bergman projection nevertheless admit a priori estimates

weighted automata and weighted logics weighted automata are used to describe quantitative properties in various areas such as probabilistic systems image compression speech to text processing the behaviour of such an automaton is a mapping called a formal power series assigning to each word a weight in some semiring we generalize buchi s and elgot s fundamental theorems to this quantitative setting we introduce a weighted version of mso logic and prove that for commutative semirings the behaviours of weighted automata are precisely the formal power series definable with particular sentences of our weighted logic we also consider weighted first order logic and show that aperiodic series coincide with the first order definable ones if the semiring is locally finite commutative and has some aperiodicity property

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

compactness of the neumann problem on convex domains the neumann operator on 0 q forms 1 q n on a bounded convex domain in cnis compact if and only if the boundary of contains no complex analytic equivalently affine variety of dimension greater than or equal toq

regularity of the neumann problem at point of infinite type abstract we introduce general estimates for gain of regularity of solutions of the neumann problem and relate it to the existence of weights with large levi form at the boundary this enables us to discuss in a unified framework the classical results on fractional ellipticity subellipticity superlogarithmic ellipticity and compactness for each case we exhibit a corresponding class of domains

sobolev estimates for the bar partial neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary

global regularity for the neumann operator and bounded plurisubharmonic exhaustion functions abstract for a smooth bounded pseudoconvex domain c n we derive a new sufficient condition for global regularity of the neumann operator that generalizes mcneal s property p the approximately holomorphic vector fields of boas and straube and a condition involving bounded plurisubharmonic exhaustion functions due to kohn