weighted lipschitz estimates for on convex domains of finite type abstract in this paper we introduce the scaled weighted growth spaces and the scaled weighted lipschitz spaces we prove the norm estimates for and the boundedness of the bergman projection in these scaled weighted function spaces on a convex domain of finite type in c n

dynamics stability and statistics on lattices and networks these lectures aim at surveying some dynamical models that have been widely explored in the recent scientific literature as case studies of complex dynamical evolution emerging from the spatio temporal organization of several coupled dynamical variables the first message is that a suitable mathematical description of such models needs tools and concepts borrowed from the general theory of dynamical systems and from out of equilibrium statistical mechanics the second message is that the overall scenario is definitely reacher than the standard problems in these fields for instance systems exhibiting complex unpredictable evolution do not necessarily exhibit deterministic chaotic behavior i e lyapunov chaos as it happens for dynamical models made of a few degrees of freedom in fact a very large number of spatially organized dynamical variables may yield unpredictable evolution even in the absence of lyapunov instability such a mechanism may emerge from the combination of spatial extension and non

a technique for realizing linear phase iir filters a real time iir filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional fir filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay iir filters this structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real time recursive implementation of the noncausal transfer function h z sup 1 the time reversed section technique used to realize exactly linear phase iir filters is described the effects of finite section length on the sectional convolution are analyzed a simulation methodology is developed to address the special requirements of simulating a time reversed section filter a design example is presented with computer simulation to illustrate performance in terms of overall magnitude response and phase linearity as a function of finite section length nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct fir implementation

the cauchy integral in cn for domains with minimal smoothness abstract we prove l p b d regularity of the cauchy leray integral for bounded domains d c n whose boundary satisfies the minimal regularity condition of class c 1 1 together with a naturally occurring notion of convexity

phase improvement in iir digital filters a new technique is presented for improving the phase response of finite impulse response iir digital filters in this technique a measure of phase nonlinearity is developed given an iir filter which has the desired amplitude response and it realized as a cascade of second order sections the measure is minimized by making some of the sections anticausal efficient implementation of this algorithm is discussed examples illustrating the technique are also given

using max entropy ratio of recurrence plot to measure electrocorticogram changes in epilepsy patients abstract a maximum entropy ratio mer method is firstly adapted to investigate the high dimensional electrocorticogram ecog data from epilepsy patients mer is a symbolic analysis approach for the detection of recurrence domains of complex dynamical systems from time series data were chosen from eight patients undergoing pre surgical evaluation for drug resistant temporal lobe epilepsy mers for interictal and ictal data were calculated and compared a statistical test was performed to evaluate the ability of mer to separate the interictal state from the ictal state mer showed significant changes from the interictal state into the ictal state where mer was low at the ictal state and is significantly different with that at the interictal state these suggest that mer is able to separate the ictal state from the interictal state based on ecog data it has the potential of detecting the transition between normal brain activity and the ictal state

zero varieties for the nevanlinna class in convex domains of finite type in mathbb c n with x ak each ak being counted according to its multiplicity in this case too it is well known that conversely the blaschke condition implies that the sequence x is the zero sequence of a function f e n q or even a bounded holomorphic function the question whether in dimension n 1 the blaschke condition b is sufficient for the divisor x xk nk to be defined by a function f e n q has been one of the main topics in this area the first result was independently obtained by henkin 11 and skoda 14 who proved it for strictly pseudoconvex domains with some obvious topological conditions also some partial results

digital filters with equiripple magnitude and group delay this paper introduces a class of recursive digital filters having equiripple behavior in both the magnitude and group delay responses the filters consist of an all pole iir component cascaded with a linear phase fir component the iir component is synthesized so that its group delay exhibits an equiripple variation in the passband whereas the fir component is used to obtain the desired equiripple nature for the amplitude response in both the passband and stopband s an iterative procedure is presented for optimizing the ripple in the group delay and the order of the iir part in such a way that the overall multiplication rate attains its minimum examples show that standard simultaneous amplitude and phase optimization methods only slightly change the results obtained using this method the new method is straightforward to implement and avoids the problems of guessing good initial values and of premature termination several examples show that the new filters require significantly fewer multipliers in narrow band applications than equivalent fir and delay equalized elliptic designs at the expense of a negligible variation in the group delay

estimates for the bergman and szego kernels in mathbf c 2 the purpose of this paper some of whose conclusions were announced in nrsw is to study the bergman and szegd projection operators on pseudoconvex domains q of finite type in c2 the results we obtain are of three kinds i the size estimates of the bergman and szeg6 kernels and their derivatives ii the cancellation properties of those kernels expressed in terms of the actions of these operators on suitable bump functions these properties have an interest in their own right but are also crucial in iii below iii the sharp mapping properties of these operators on functions spaces such as lp the nonisotropic sobolev spaces and the nonisotropic lipschitz spaces which are naturally attached to the geometry of the boundary this also leads ultimately to sharp results in the regularity properties of solutions of the equation du f in q and 9bu f on the boundary let us describe these matters in more detail our starting points are certain basic geometric constructs associated to q a metric p defined in terms of the vector fields x1 and x2 which are the real and imaginary parts of the tangential levi vector field on d 2 and a function a p 8 a polynomial in 8 for p e d 2 which represents the higher levi invariant attached to d 9 the significance of these to the geometry of d q can be understood from the following facts the ball b p 8 c d q centered at p of radius 8 in the metric p when viewed in the appropriate coordinates has width 8 in the complex tangential directions but its width is a p 8 in the complementary direction thus the volume of the ball is 82a p 8 among other crucial properties

plurisubharmonic polynomials and bumping we wish to study the problem of bumping outwards a pseudoconvex finite type domain omega subset mathbb c n in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with at the site of the bumping are explicitly realised generally when omega subset mathbb c n n geq 3 the known methods lead to bumpings with high orders of contact which are not explicitly known either at the site of the bumping precise orders are known for h extendible semiregular domains this paper is motivated by certain families of non semiregular domains in mathbb c 3 these families are identified by the behaviour of the least weight plurisubharmonic polynomial in the catlin normal form accordingly we study how to perturb certain homogeneous plurisubharmonic polynomials without destroying plurisubharmonicity

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

estimates for the neumann problem for pseudoconvex domains in c2 of finite type abstract we outline results obtained for the neumann problem for an arbitrary pseudoconvex domain in c2 of finite type we obtain an approximation to the neumann operator a number of sharp estimates for the solution of u f are a consequence one of these is an extension of the l1 estimate of henkin and skoda used to characterize the zero sets of functions of the nevanlinna class

convex hypersurfaces and fourier transforms hilbert transforms and maximal functions along curves and surfaces spectral synthesis problems and the study of certain operators related to hyperbolic partial differential and pseudodifferential operators the problem of estimating such fourier transforms has a long history see for example hlawka 3 herz 2 littman 4 randol 9 10 svensson 15 sogge and stein 12 13 stein 14 marshall 5 etc the results of these investigations suggest a strong relation between the local curvature properties of the surface s and the decay of the function a we are mainly interested in how the geometry of s near a fixed point xo affects the decay of a6 for by using a partition of unity on s it is clearly enough to study integrals of the type

a solution operator for bar partial on the hartogs triangle and l p lp estimates an integral solution operator for bar partial is constructed on product domains that include the punctured bidisc this operator is shown to satisfy l p estimates for all 1 le p infty though with non standard relative to strongly pseudoconvex domains bounding term these estimates imply l p estimates for bar partial on the hartogs triangle with greater range of p than the canonical solution satisfies

linear phase iir filter with equiripple stopband a simple technique of introducing transmission zeros into a low pass all pole filter function to make its stopband transmission equiripple is described the zeros are introduced through a transformation which maps the stopband of the filter onto the unit circle and the passband onto a segment of the real axis in the transformed plane the technique is used to improve the loss characteristic of all pole constant delay filters examples are included to illustrate the design procedure

supnorm and f holder estimates for on convex domains of general type in c2 abstract in this paper we study supnorm and modified holder estimates for the integral solution of the equation on a class of convex domains of general type in c 2 that includes many infinite type examples

iir digital filters with equiripple stopband transmission recently a simple technique of introducing transmission zeros into a low pass all pole filter transfer function to make its stop band transmission equiripple has been described by hazra 1 it is shown that this technique represents a special case of a more general procedure which provides not only hazra s solution but also additional filters which are advantageous with regard to the required number of multiplications per sample the results are demonstrated with the aid of an example

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis structures in recurrence plots rps preserving the rich information of nonlinear invariants and trajectory characteristics have been increasingly analyzed in dynamic discrimination studies the conventional analysis of rps is mainly focused on quantifying the overall diagonal and vertical line structures through a method called recurrence quantification analysis rqa this study extensively explores the information in rps by quantifying local complex rp structures to do this an approach was developed to analyze the combination of three major rqa variables determinism laminarity and recurrence rate dlr in a metawindow moving over a rp it was then evaluated in two experiments discriminating 1 ideal nonlinear dynamic series emulated from the lorenz system with different control parameters and 2 data sets of human heart rate regulations with normal sinus rhythms n 18 and congestive heart failure n 29 finally the dlr was compared with seven major rqa variables in terms of discriminatory power measured by standardized mean difference d smd in the two experiments dlr resulted in the highest discriminatory power with d smd 2 53 and 0 98 respectively which were 7 41 and 2 09 times the best performance from rqa the study also revealed that the optimal rp structures for the discriminations were neither typical diagonal structures nor vertical structures these findings indicate that local complex rp structures contain some rich information unexploited by rqa therefore future research to extensively analyze complex rp structures would potentially improve the effectiveness of the rp analysis in dynamic discrimination studies

convex domains of finite type we construct bounded plurisubharmonic functions with maximally large hessians near the boundary of a smoothly bounded convex domain in cn as a corollary the equality of the order of contact of the boundary with complex analytic varieties the d angelo type and the order of contact with complex lines is demonstrated

an integral kernel for weakly pseudoconvex domains a new explicit construction of cauchy fantappie kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary while not holomorphic in the parameter the new kernel reflects the complex geometry and the levi form of the boundary some estimates are obtained for the corresponding integral operator which provide evidence that this kernel and related constructions give useful new tools for complex analysis on this general class of domains

holder estimates for homotopy operators on strictly pseudoconvex domains with c 2 boundary we derive a new homotopy formula for a strictly pseudoconvex domain of c 2 boundary in mathbf c n by using a method of lieb and range and obtain estimates in lipschitz spaces for the homotopy operators for r 1 and q 0 we obtain a lambda r 1 2 solution u to overline partial u f for a overline partial closed 0 q form f of class lambda r in the domain we apply the estimates to obtain boundary regularities of mathcal d solutions for a domain in mathbf c n times mathbf r m

measuring nonstationarity by analyzing the loss of recurrence in dynamical systems we propose a measure for nonstationarity which is based on the analysis of distributions of temporal distances of neighboring vectors in state space as an extension of previous techniques our method does not require a partitioning of the time series moreover the deviation of mean recurrence times from frequency distributions that would be expected under stationary conditions allows us to estimate the statistical significance of the method

estimates for the parametrix of the kohn laplacian on certain domains soit le demi espace superieur degenere generalise dans c 3 d p w 1 w 2 w imw p w 1 w 2 2 ou p c p 0 0 p est reel p 0 p 0 0 k p 0 0 pour k 2 on etudie la taille de la solution fondamentale de b sur des formes 0 1 sur la frontiere de d p