hua operators poisson transform and relative discrete series on line bundles over bounded symmetric domains let d g k be a bounded symmetric domain and s k l be its shilov boundary we consider the action of g with weight nu in mathbb z on functions on d viewed as sections the line bundle and the corresponding eigenspace of g invariant di erential operators the poisson transform maps hyperfunctions on the s to the eigenspaces we characterize the image in terms of hua operators on the sections of the line bundle for some special parameter the poisson transform is of szego type mapping into the relative discrete series we compute the corresponding elements in the discrete series

shimura invariant differential operators and their eigenvalues let bar d be the covariant cauchy riemann operator and mathcal d the covariant holomorphic differential operator on a line bundle over a hermitian symmetric space g k we study the shimura invariant differential operators defined via bar d and mathcal d we find the eigenvalues of a family of the shimura operators and of the generators

lagrangian coherent structures and mixing in two dimensional turbulence abstract we introduce a lagrangian definition for the boundaries of coherent structures in two dimensional turbulence the boundaries are defined as material lines that are linearly stable or unstable for longer times than any of their neighbors such material lines are responsible for stretching and folding in the mixing of passive tracers we derive an analytic criterion that can be used to extract coherent structures with high precision from numerical or experimental data sets the criterion provides a rigorous link between the lagrangian concept of hyperbolicity the okubo weiss criterion and vortex boundaries we apply the results to simulations of two dimensional barotropic turbulence

on the validity of the weiss criterion in two dimensional turbulence abstract the weiss criterion for two dimensional incompressible turbulent flows separates flow regions where the motion is hyperbolic in character from regions where it is elliptic this criterion is based on the hypothesis that the velocity gradient varies slowly with respect to the vorticity gradient we inspected this hypothesis and derived a criterion linking its validity to the curvature of the pressure field it turns out from numerical experiments that the hypothesis on which relies the weiss criterion is nearly only valid in vortex cores that is in strongly elliptic regions and near stagnation points high pressures

rankin selberg without unfolding and bounds for spherical fourier coefficients of maass forms in this paper we study periods of automorphic functions we present a new method which allows one to obtain non trivial spectral identities for weighted sums of certain periods of automorphic functions these identities are modelled on the classical identity of r rankin ra and a selberg se we recall that the rankinselberg identity relates the weighted sum of fourier coefficients of a cusp form to the weighted integral of the inner product of with the eisenstein series e g formula 1 7 below we show how to deduce the classical rankin selberg identity and similar new identities from the uniqueness principle in representation theory also known under the following names the multiplicity one property gelfand pair the uniqueness principle is a powerful tool in representation theory it plays an important role in the theory of automorphic functions we associate a non trivial spectral identity to certain pairs of different triples of gelfand subgroups namely we associate a spectral identity see formula 1 4 below with two triples f h1 g and f h2 g of subgroups in a group g such that pairs g hi and hi f for i 1 2 are strong gelfand pairs having the same subgroup f in the intersection for the notion of gelfand pair that we use see section 1 1 3 we call such a collection g h1 h2 f a strong gelfand formation in the introduction we explain our general idea and describe how to implement it in order to reprove the classical rankin selberg formula we also obtain a new anisotropic analog of the rankin selberg formula we present then an analytical application of these spectral identities towards non trivial bounds for various fourier coefficients of cusp forms the novelty of our results lies mainly in the method as we do not rely on the well known technique of rankin and selberg

harmonic analysis for spinor fields in complex hyperbolic spaces abstract l2 harmonic analysis for dirac spinors on the complex hyperbolic space hn c is developed the spinor spherical functions are calculated in terms of jacobi functions the plancherel and paley wiener theorems for the spherical transform are obtained by reduction to jacobi analysis we demonstrate analytically the existence of harmonic l2 spinors in the case of n even the action of the invariant differential operators on the poisson transforms is given explicitly

l infty norms of eigenfunctions of arithmetic surfaces here and elsewhere a l1o0 as a xc is a basic problem of quantum chaos s in any case almost nothing beyond 0 2 is known about 110 joc when the curvature is negative one can push the standard techniques and replace a1 4 by a1 4 log a in this case in this paper we use arithmetic techniques in particular modular correspondences to obtain the first improvement in the exponent 0 2 we also obtain lower bounds on the l norms in these arithmetic cases in more detail let a b be a quaternion division algebra over q a is linearly generated by 1 w q wq over q and w2 a q2 b wq qw 0 here a b e z are square free and we will assume that a 0 as usual the norm and trace are defined by n a a d tr a a oy where if a xo x1w x2q x3wq

oscillation control in non linear systems using a first order filter in this paper we shall address the oscillation control problems in certain classes of non linear systems whose outputs are required to follow their inputs it is assumed that the non linear systems can be well represented by a set of state space equations and undergo hopf bifurcation at some particular value of their parameters or their inputs a simple first order output feedback controller is proposed for oscillation control in these non linear systems first it is shown that in most cases the first order controller is effective in locally stabilizing a second order non linear system which is undergoing hopf bifurcation then a state separation method based on the solution of the associated riccati equation is applied to the oscillation control of higher order non linear systems and a second order approximated model is developed for the purpose of designing an oscillation controller the closed loop stability of the reduced order model based design is analysed and some sufficient stability conditions ar

a paley wiener theorem for real reductive groups le groupe sl 3 r prequantification des orbites de dimension minimale parmi celles non triviales dans la representation co adjointe de sl 3 r noyaux de blattner kostant steinberg irreductibilite et unicite du prolongement de certaines representations de p 3 a sl 3 r etude du prolongement des representations e a sl 3 r la representation type s s 2 minimal parametres de langlands et operateur d entrelacement avec la serie principale pour les representations e et

branching problems in reproducing kernel spaces for a semisimple lie group g satisfying the equal rank condition the most basic family of unitary irreducible representations is the discrete series found by harish chandra in our work here we study some of the branching laws for discrete series when restricted to a subgroup h of the same type by combining classical results with recent work of kobayashi in particular we prove discrete decomposability under harish chandra s condition of cusp form on the reproducing kernel we show a relation between discrete decomposability and representing certain intertwining operators in terms of differential operators

the plancherel formula for spherical functions with a one dimensional k type on a simply connected simple lie group of hermitian type abstract we generalize the harish chandra inversion formula for the spherical transform on a riemannian symmetric space to homogeneous line bundles on a hermitian symmetric space we determine the plancherel measure explicitly

the equivalence of time scale decomposition techniques used in the analysis and design of linear systems linear system models can be decomposed into reduced order fast and slow subsystems using spectrum separating solutions to dual riccati type equations eigenspace power iterations provide globally convergent iterative schemes for obtaining these solutions from this basis an equivalence of previous decomposition techniques is then achieved including the classic two time scale asymptotic series decomposition of singularly perturbed systems the result is a unified theory for the decomposition of time scales in linear systems applicable to both continuous and discrete time models

nearly holomorphic sections on compact hermitian symmetric spaces abstract let x be a kahler manifold and e be a hermitian vector bundle on x we investigate the space n x e of nearly holomorphic sections in e which generalizes the notion of nearly holomorphic functions introduced by shimura if x u k is a compact hermitian symmetric space and e is u homogeneous it turns out that n x e coincides with the space of u finite vectors in c x e and we obtain new results on the u type decomposition of the hilbert space of square integrable sections as an application we determine this decomposition for the holomorphic tangent bundle of x

subconvex bounds for hecke maass forms on compact arithmetic quotients of semisimple lie groups let h be a semisimple algebraic group k a maximal compact subgroup of g h mathbb r and gamma subset h mathbb q a congruence arithmetic subgroup in this paper we generalize existing subconvex bounds for hecke maass forms on the locally symmetric space gamma backslash g k to corresponding bounds on the arithmetic quotient gamma backslash g for cocompact lattices using the spectral function of an elliptic operator the bounds obtained extend known subconvex bounds for automorphic forms to non trivial k types yielding such bounds for new classes of automorphic representations they constitute subconvex bounds for eigenfunctions on compact manifolds with both positive and negative sectional curvature we also obtain new subconvex bounds for holomorphic modular forms in the weight aspect

a multivariate version of the disk convolution abstract we present an explicit product formula for the spherical functions of the compact gelfand pairs g k 1 su p q su p su q with p 2 q which can be considered as the elementary spherical functions of one dimensional k type for the hermitian symmetric spaces g k with k s u p u q due to results of heckman they can be expressed in terms of heckman opdam jacobi polynomials of type bc q with specific half integer multiplicities by analytic continuation with respect to the multiplicity parameters we obtain positive product formulas for the extensions of these spherical functions as well as associated compact and commutative hypergroup structures parametrized by real p 2 q 1 we also obtain explicit product formulas for the involved continuous two parameter family of heckman opdam jacobi polynomials with regular but not necessarily positive multiplicities the results of this paper extend well known results for the disk convolutions for q 1 to higher rank

robustness measures for linear systems with application to stability radii of hurwitz and schur polynomials in this paper we consider robustness measures stability radii for system matrices which are subjected to structured real and complex perturbations of the form a a bdc where b c are given matrices our object is twofold a to present a number of new results mainly concerning the real stability radius and its differences from the complex one b to give an overview of our approach to the robustness analysis of linear state space systems including basic properties and characterizations of the complex stability radius applying the results to the special case where a is in companion form and b 0 0 0 1 t we are able to determine stability radii for hurwitz and schur polynomials under arbitrary complex and real affine perturbations of the coefficient vector computable formulae are obtained and illustrated by several examples

plancherel formula for berezin deformation of l 2 on riemannian symmetric space consider natural representations of the pseudounitary group u p q in the space of holomorphic functions on the cartan domain hermitian symmetric space u p q u p u q berezin representations of o p q are the restrictions of such representations to the subgroup o p q we obtain the explicit plancherel formula for the berezin representations the support of the plancherel measure is a union of many series of representations the density of the plancherel measure on each piece of the support is an explicit product of functions we also show that the berezin representations give an interpolation between l2 on noncompact symmetric space o p q o p o q and l2 on compact symmetric space o p q o p o q

bounding sup norms of cusp forms of large level let f be an l2 normalized weight zero hecke maas cusp form of square free level n character and laplacian eigenvalue 1 4 it is shown that f n 1 37 from which the hybrid bound f 1 4 n for some 0 is derived the first bound holds also for f yk 2f where f is a holomorphic cusp form of weight k with the implied constant now depending on k

particle segregation by stokes number for small neutrally buoyant spheres in a fluid it is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers due to the inertia of the particle the planar dynamics are described in a four dimensional phase space and thus can differ considerably from the ideal tracer dynamics using finite time lyapunov exponents we compute the sensitivity of the final position of a particle with respect to its initial velocity relative to the fluid and thus partition the relative velocity subspace at each point in configuration space the computations are done at every point in the relative velocity subspace thus giving a sensitivity field the stokes number being a measure of the independence of the particle from the underlying fluid flow acts as a parameter in determining the variation in these partitions we demonstrate how this partition framework can be used to segregate particles by stokes number in a fluid the fluid model used for demonstration is a two dimensional cellular flow

boundary value problems for various boundaries of hermitian symmetric spaces abstract the image of the poisson transform on a principal series representations on a boundary component of a hermitian symmetric space is considered we prove that the image is characterized by a covariant differential operator on a homogeneous line bundle on the symmetric space

boundary value problems for the shilov boundary of a bounded symmetric domain of tube type abstract in this article the images of the poisson transform on the degenerate series representations attached to the shilov boundary of a bounded symmetric domain of tube type are considered we characterize the images by means of second order differential equations

l2 concrete spectral analysis of the invariant laplacianδαβin the unit complex ballbn for every fixed real number related to the continuous spectrum of the invariant laplacians 4 1 z 2 i j 1n ij zizj 2 zj zj j 1nzj zj j 1nzj zj inbn we characterize the eigenfunctions of that are poisson integrals ofl2 functions on the boundary ofbn these eigenfunctions occurred in the weighted plancherel formula of the unit complex ball see zhang studia math 102 2 1992 for the weighted plancherel formula in the ball the obtained characterization generalizes our announced result in boussejra and intissar c r acad sci 315 1992 1353 1357 for the bergman laplacian 00of the unit complex ball to the laplacians for arbitrary inr

bifurcation control of a chaotic system the viability of controlling chaos by controlling associated bifurcations is demonstrated in the context of a thermal convection loop model washout filter aided feedback controls are employed to delay and to extinguish chaos in the model and to target preferred equilibrium points an important feature of the control laws is that they do not result in any change in the set of equilibria even in the presence of model uncertainty

where do inertial particles go in fluid flows abstract we derive a general reduced order equation for the asymptotic motion of finite size particles in unsteady fluid flows our inertial equation is a small perturbation of passive fluid advection on a globally attracting slow manifold among other things the inertial equation implies that particle clustering locations in two dimensional steady flows can be described rigorously by the q parameter i e by one half of the squared difference of the vorticity and the rate of strain use of the inertial equation also enables us to solve the numerically ill posed problem of source inversion i e locating initial positions from a current particle distribution we illustrate these results on inertial particle motion in the jung tel ziemniak model of vortex shedding behind a cylinder in crossflow

sparse equidistribution problems period bounds and subconvexity we introduce a geometric method to bound periods of automorphic forms the key features of this method are the use of equidistribution results in place of mean value theorems and the systematic use of mixing and the spectral gap applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of cm points to subconvexity of the triple product period in the level aspect over number fields which implies subconvexity for certain standard and rankin selberg l functions and to bounding fourier coefficients of automorphic forms

the sup norm problem on the siegel modular space of rank two let f be a square integrable maa ss form on the siegel upper half space mathcal h of rank 2 for the siegel modular group rm sp 4 bbb z with laplace eigenvalue lambda if in addition f is a joint eigenfunction of the hecke algebra and omega is a compact set in rm sp 4 bbb z backslash mathcal h we show the bound f omega infty ll omega 1 lambda 1 delta for some global constant delta0 as an auxiliary result of independent interest we prove new uniform bounds for spherical functions on semisimple lie groups