existence and multiplicity results for a class of generalized one dimensional p laplacian problem abstract in this paper we study a class of one dimensional p laplacian boundary value problem with generalized sturm liouville boundary conditions some results are obtained for existence of at least three positive solutions by using the related fixed point theory the interesting point is the nonlinear term f which involves the first order derivative explicitly

successive iteration and positive pseudo symmetric solutions for a three point second order p laplacian boundary value problems in this paper we study the existence of positive pseudo symmetric solutions for a three point second order p laplacian boundary value problems with dependence on the first order derivative by applying a monotone iterative method

multiple results of p laplacian dynamic equations on time scales in this paper a new fixed point theorem introduced by avery and peterson and another fixed point theorem are applied to boundary value problems for p laplacian dynamic equations on time scales by imposing some growth conditions on the nonlinearity f we establish the existence results of at least three positive solutions as an application some examples are included to illustrate the main results

existence of symmetric positive solutions for a class of sturm liouville like boundary value problems this paper deals with the existence of symmetric positive solutions for a class of singular sturm liouville like boundary value problems with a one dimensional p laplacian operator by using the fixed theorem of cone expansion and compression of norm type in a cone the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function

symmetric positive solutions to singular system with multi point coupled boundary conditions in this paper we study the existence and multiplicity of symmetric positive solutions for a nonlinear system with multi point coupled boundary conditions the arguments are based upon a specially constructed cone and the fixed point index theorem in cones an example is then given to demonstrate the applicability of our results

spherical unitary highest weight representations in this paper we give an almost complete classification of the h spherical unitary highest weight representations of a hermitian lie group g where g h is a symmetric space of cayley type

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

nonlinear eigenvalue problems for quasilinear systems the paper deals with the existence of positive solutions for the quasilinear system f u lh t f u 0 0 1 h t diag h 1 t h n t and f u f 1 u f n u assume that f i and h i are nonnegative continuous for u u 1 u n let f 0 i lim u 0f i u f u f i lim u f i u f u i 1 n f 0 maxf 1 0 f n 0 and f maxf 1 f n we prove that the boundary value problem has a positive solution for certain finite intervals of l if one of f 0 and f is large enough and the other one is small enough our methods employ fixed point theorem in a cone

restriction to symmetric subgroups of unitary representations of rank one semisimple lie groups we consider the spherical complementary series of rank one lie groups h n so0 n 1 f for f r c h we prove that there exist finitely many discrete components in its restriction under the subgroup hn 1 so0 n 1 1 f this is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of g n su n 1 su n 1 x su n 1 and su 2n 2 and by the branching of holomorphic representations under the corresponding subgroup g n 1

kahler einstein submanifolds of the infinite dimensional projective space this paper consists of two main results in the first one we describe all kahler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the wallach set of the domain in the second one we exhibit an example of complete and non homogeneous kahler einstein metric with negative scalar curvature which admits a kahler immersion into the infinite dimensional complex projective space

multiple fixed sign solutions for a system of difference equations with sturm liouville conditions we consider the following system of difference equations d mu i k p i k u 1 k u 2 k u n k 0 k 0 1 n i 1 2 ntogether with sturm liouville boundary conditions d ju i 0 0 0 2 n m 1 z 0 w 0 h 0 d w z w n 1 z d h w 0 by using two different fixed point theorems we develop criteria for the existence of three solutions of the system which are of fixed signs on 0 1 n m examples are also included to illustrate the results obtained

holomorphic isometries of mathbb b m into bounded symmetric domains arising from linear sections of minimal embeddings of their compact duals we study general properties of images of holomorphic isometric embeddings of complex unit balls mathbb b m into irreducible bounded symmetric domains varomega of rank at least 2 in particular we show that such holomorphic isometries with the minimal normalizing constant arise from linear sections varlambda of the compact dual x c of varomega the question naturally arises as to which linear sections z varlambda cap varomega are actually images of holomorphic isometries of complex unit balls we study the latter question in the case of bounded symmetric domains varomega of type iv alias lie balls i e bounded symmetric domains dual to hyperquadrics we completely classify images of all holomorphic isometric embeddings of complex unit balls into such bounded symmetric domains varomega especially we show that there exist holomorphic isometric embeddings of complex unit balls of codimension 1 incongruent to the examples constructed by mok proc am math soc 144 4515 4525 2016 from varieties of minimal rational tangents and that moreover any holomorphic isometric embedding f mathbb b m rightarrow varomega extends to a holomorphic isometric embedding f mathbb b n 1 rightarrow varomega dim varomega n the case of lie balls is particularly relevant because holomorphic isometric embeddings of complex unit balls of sufficiently large dimensions into an irreducible bounded symmetric domain other than a type iv domain are expected to be more rigid

hemivariational inequality for viscoelastic contact problem with slip dependent friction abstract in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction law is described by a multivalued subdifferential relation which includes the slip displacement dependent friction and the tresca models we establish the existence of weak solutions to the problem by using a surjectivity result for pseudomonotone mappings

dynamic bilateral contact problem for viscoelastic piezoelectric materials with adhesion abstract a model of a dynamic viscoelastic adhesive contact between a piezoelectric body and a deformable foundation is described the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential and the ordinary differential equation for the adhesion field in the hemivariational inequality the friction forces are derived from a nonconvex superpotential through the generalized clarke subdifferential the existence of a weak solution is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

homogeneous tuples of multiplication operators on twisted bergman spaces letbthe bergman kernel on the domain n mofn mcontractive complex matrices m n 1 let w wn mbe the associated wallach set consisting of the 0 for whichb m n is non negative definite and hence the reproducing kernel of a functional hilbert space h for w we examine themn tuplem of operators on h whose components are multiplications by themnco ordinate functions this tuple is homogeneous with respect to the group action ofpsu n m on the matrix ball utilising this group action we are able to determine the set of all w for which i m is bounded and for which ii m is bounded and jointly subnormal further the joint taylor spectrum ofm is determined for all as in i the subnormality ofm turns out to be closely tied with the representation theory ofpsu n m namely m is subnormal precisely when the natural projective representation ofpsu n m on the twisted bergman space h is a subrepresentation of an induced representation of multiplicity 1 finally we examine the values of for whichm admits its taylor spectrum as ak spectral set and obtain incomplete results on this question this question remains open and interesting onn 1 gaps that is for belonging to the union ofn 1 pairwise disjoint open intervals most of the techniques developed in this paper are applicable to all bounded cartan domains though we stick to the matrix domains n mfor concreteness

existence of triple positive solutions of two point right focal boundary value problems on time scales we consider the following boundary value problem 1 n 1y d n t 1 p 1f t y s n 1 t email protected a b t y d n a 0 email protected email protected p 1 y d n s b 0 email protected email protected n 1 where n 2 1 p n 1 is fixed and t is a time scale by applying fixed point theorems for operators on a cone existence criteria are developed for triple positive solutions of the boundary value problem we also include examples to illustrate the usefulness of the results obtained

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

slip dependent friction in dynamic elasticity the dynamic evolution with frictional contact of an elastic body is considered in modeling the contact the tresca model and a slip dependent friction law are used the existence of a solution is proved in the two dimensional case the uniqueness is proved for the one dimensional shearing problem the convergence for a vanishing viscosity of the unique solution of the viscoelastic problem to a solution of the elastic problem is obtained

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on time scales in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value pr

fonctions holomorphes a croissance moderee et vecteurs distributions the space of distribution vectors of a holomorphic discrete series representation of scalar type can be identified to a space of holomorphic functions with moderate growth this is the main result of the paper we give an application of it to the hankel transform and to multivariate laguerre series expansions

positive solutions for p laplacian functional dynamic equations on time scales abstract in this paper the authors study the boundary value problems for a p laplacian functional dynamic equation on a time scale p x t a t f x t x t 0 t 0 t x 0 t t t r 0 x 0 b 0 x 0 x t 0 by using the twin fixed point theorem sufficient conditions are established for the existence of twin positive solutions

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian p x t q t f t x t x t 0 t 0 1 subject to one of the following boundary conditions p x 0 p x 0 0 p x 1 p x 1 0 or x 0 g1 x 0 0 x 1 g2 x 1 0 where p s s p 2s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions the interesting point is the nonlinear term f is involved with the first order derivative explicitly

necessary and sufficient conditions for the existence of quasi symmetric positive solutions of singular boundary value problem abstract this paper investigates the existence of quasi symmetric positive solutions for fourth order singular three point boundary value problem we first give definitions of quasi symmetric lower and upper solutions by constructing quasi symmetric lower and upper solutions and using the schauder fixed point theorem necessary and sufficient conditions for existence results are obtained

multiple positive solutions for m point boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary conditions u 0 i 1 m 2 a i u i u 1 i 1 m 2 b i u i where p s s p 2 s by using a fixed point theorem in a cone we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem

tensor products of holomorphic representations and bilinear differential operators let h be the weighted bergman space on a bounded symmetric domain d g k it has analytic continuation in the weight and for in the so called wallach set h still forms unitary irreducible projective representations of g we give the irreducible decomposition of the tensor product h 1 h 2 of the representations for any two unitary weights and we find the highest weight vectors of the irreducible components we find also certain bilinear differential intertwining operators realizing the decomposition and they generalize the classical transvectants in invariant theory of sl 2 c as applications we find a generalization of the bol s lemma and we characterize the multiplication operators by the coordinate functions on the quotient space of the tensor product h 1 h 2 modulo the subspace of functions vanishing of certain degree on the diagonal

positive solutions for a fourth order p laplacian boundary value problem abstract in this paper we study the existence multiplicity and uniqueness of positive solutions for the fourth order p laplacian boundary value problem u p 1 u f t u u 2 i 0 u 2 i 1 0 i 0 1 here p 0 and f c 0 1 r r r 0 based on a priori estimates achieved by utilizing properties of concave functions we use fixed point index theory to establish our main results

function theory on cartan domains and the berezin toeplitz symbol calculus cn with dv z normalized lebesgue measure on 9 we let l l2 q dv be the usual space of lebesgue square integrable complex valued functions on 9 by h2 h2 q dv we denote the bergman subspace of l2 consisting of holomorphic functions the orthogonal projection operator from l2 onto h2 is denoted by p forf in l q the space of essentially bounded measurable functions on 9 we will consider the multiplication operator

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the contact is modeled by a general normal damped response condition and a friction law which are nonmonotone possibly multivalued and have the subdifferential form the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

three solutions for three point boundary value problems abstract in this paper we study the existence of at least three solutions for the three point nonlinear boundary value problems u t a t f u 0 0 t 1 u 0 0 u 1 u where 0 1 0 1 a c 0 1 0 and f c r r without any monotonicity assumptions on the nonlinear term f by using the increasing operator theory and approximation process we prove that the three point boundary value problems has at least three solutions

three positive solutions of boundary value problems for p laplacian difference equations in this paper existence criteria for three positive solutions of p laplacian difference equation f p u t 1 a t f u t 0 t 1 t 1 u 0 u t 2 0 oru 0 u t 1 0 are established by using the five functionals fixed point theorem as an application one example is given to illustrate the main result in this paper

three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales abstract the five functionals fixed point theorem is applied to investigate the existence of at least three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales

commuting toeplitz operators on bounded symmetric domains and multiplicity free restrictions of holomorphic discrete series abstract for any given bounded symmetric domain we prove the existence of commutative c algebras generated by toeplitz operators acting on any weighted bergman space the symbols of the toeplitz operators that generate such algebras are defined by essentially bounded functions invariant under suitable subgroups of the group of biholomorphisms of the domain these subgroups include the maximal compact groups of biholomorphisms we prove the commutativity of the toeplitz operators by considering the bergman spaces as the underlying space of the holomorphic discrete series and then applying known multiplicity free results for restrictions to certain subgroups of the holomorphic discrete series in the compact case we completely characterize the subgroups that define invariant symbols that yield commuting toeplitz operators in terms of the multiplicity free property

quantum riemann surfaces i the unit disc we construct a non commutative algebra c mu bar u which is a quantum deformation of the algebra of continuous functions on the closed unit disc bar u c mu bar u is generated by the toeplitz operators on a suitable hilbert space of holomorphic functions onu

operator valued bessel functions holomorphic discrete series and harmonic representations of u p q abstract this paper presents representation theoretic applications of the theory of operator valued bessel functions which was developed in the first paper of this series using the reduced bessel function k we study the harmonic representation and holomorphic discrete series for the group u p q of biholomorphic automorphisms of the siegel domains of type ii

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

triple positive solutions of boundary value problems for p laplacian dynamic equations on time scales a new triple fixed point theorem is applied to investigate the existence of at least three positive solutions of boundary value problems for p laplacian dynamic equations on time scales

degenerate principal series representations and their holomorphic extensions let x h l be an irreducible real bounded symmetric domain realized as a real form in an hermitian symmetric domain d g k the intersection s of the shilov boundary of d with x defines a distinguished subset of the topological boundary of x and is invariant under h it can be realized as s h p for certain parabolic subgroup p of h we study the spherical representations of h induced from p we find formulas for the spherical functions in terms of the macdonald hypergeometric function this generalizes the earlier result of faraut koranyi for hermitian symmetric spaces d we consider a class of h invariant integral intertwining operators from the representations on l2 s to the holomorphic representations of g restricted to h we construct a new class of complementary series for the groups h so n m su n m with n m 2 and sp n m with n m 1 we realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of g su n m su n m su n m and su 2n 2m respectively

multiple positive solutions for p laplacian functional dynamic equations on time scales abstract the authors improve some well known fixed point theorems and study the boundary value problems for a p laplacian functional dynamic equation on a time scale p x t a t f x t x t 0 t 0 t x 0 t t t r 0 x 0 b 0 x 0 0 x t 0 by using the fixed point theorems sufficient conditions are established for the existence of multiple positive solutions

evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction and the tresca models the existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings

complete monotonicity for inverse powers of some combinatorially defined polynomials we prove the complete monotonicity on 0 infty n for suitable inverse powers of the spanning tree polynomials of graphs and more generally of the basis generating polynomials of certain classes of matroids this generalizes a result of szeg and answers among other things a long standing question of lewy and askey concerning the positivity of taylor coefficients for certain rational functions our proofs are based on two ab initio methods for proving that p beta is completely monotone on a convex cone c the determinantal method and the quadratic form method these methods are closely connected with harmonic analysis on euclidean jordan algebras or equivalently on symmetric cones we furthermore have a variety of constructions that given such polynomials can create other ones with the same property among these are algebraic analogues of the matroid operations of deletion contraction direct sum parallel connection series connection and 2 sum the complete monotonicity of p beta for some beta 0 can be viewed as a strong quantitative version of the half plane property hurwitz stability for p and is also related to the rayleigh property for matroids

laplace and segal bargmann transforms on hermitian symmetric spaces and orthogonal polynomials let d g k be a complex bounded symmetric domain of tube type in a complex jordan algebra v and let dr j d d be its real form in a formally real euclidean jordan algebra j v dr h l is a bounded realization of the symmetric cone in j we consider representations of h that are gotten by the generalized segal bargmann transform from a unitary g space of holomorphic functions on d to an l2 space on dr we prove that in the unbounded realization the inverse of the unitary part of the restriction map is actually the laplace transform we find the extension to d of the spherical functions on dr and find their expansion in terms of the l spherical polynomials on d which are jack symmetric polynomials we prove that the coefficients are orthogonal polynomials in an l2 space the measure being the harish chandra plancherel measure multiplied by the symbol of the berezin transform we prove the difference equation and recurrence relation for those polynomials by considering the action of the lie algebra and the cayley transform on the polynomials on d finally we use the laplace transform to study generalized laguerre functions on symmetric cones

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian f p x t q t f t x t x t 0 t 0 1 subject to the following boundary value conditions x 0 i 1n a ix x i x 1 i 1n b ix x i where f p s s p 2 s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem

positive solutions for a system of second order quasilinear boundary value problems abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order quasilinear boundary value problems u p 1 f t u v v q 1 g t u v u 0 u 1 0 v 0 v 1 0 where p q 1 and f g c 0 1 r 2 r r 0 based on a priori estimates achieved by utilizing jensen s inequality for nonnegative concave functions and homogeneous operators we use fixed point index theory to establish the main results

triple positive pseudo symmetric solutions of three point bvps for p laplacian dynamic equations on time scales abstract let t be a time scale such that 0 t t we consider the three point boundary value problem for p laplacian dynamic equations on time scales t of the form p u t h t f t u t 0 for t 0 t t with boundary conditions u 0 0 u u t where t is symmetric in t t and p u u p 2 u with p 1 by using a pseudo symmetric technique and the five functionals fixed point theorem we prove that the boundary value problem has at least three positive pseudo symmetric solutions under some assumptions as an application an example is given to illustrate the result

triple positive solutions for boundary value problems on infinite intervals abstract this paper deals with the existence of triple positive solutions for sturm liouville boundary value problems of second order nonlinear differential equation on a half line by using a fixed point theorem in a cone due to avery peterson we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term

hypergeometric functions associated to cones of convex type in a euclidean jordan algebra abstract in this paper we study a family of hypergeometric functions associated to cones of convex type in a euclidean jordan algebra we obtain upper and lower bounds and give information about their singularities the family under consideration was introduced by sahi invent math 110 1992 409 418 and it plays an important role in the construction of some small representations

weyl quantization of symmetric spaces i hyperbolic matrix domains abstract it is shown that the generalized weyl calculus on the hyperbolic matrix domains defined by integration over a field of symmetries leads to bounded operators when the symbol is laplace bounded i e remains bounded after certain invariant differential operators higher laplacians are applied

toeplitz operators on bounded symmetric domains in this paper jordan algebraic methods are applied to study toeplitz operators on the hardy space h2 s associated with the shilov boundary s of a bounded symmetric domain d in c of arbitrary rank the jordan triple system z c associated with d is used to determine the relationship between toeplitz operators and differential operators further it is shown that each jordan triple idempotent e e z induces an irreducible representation e symbol of the c algebra generated by all toeplitz operators tf with continuous symbol function f 0 introduction toeplitz operators on the boundary t aa of the open unit disc a c c play an important role in function theory of one complex variable cf 9 chapter 7 in several dimensions toeplitz operators have been mainly studied for strictly pseudo convex domains d c c 4 13 14 24 28 in particular for the hilbert ball 7 using the relationship with pseudo differential operators another class of domains in c generalizing the unit disc is the class of bounded symmetric domains cartan domains and exceptional domains which have a more complicated boundary structure compared to the strictly pseudo convex case the aim of this paper is the study of toeplitz operators t1 with continuous symbol functionf e c s on the shilov boundary s of a bounded symmetric domain d of arbitrary rank r in the special cases of the hilbert ball r 1 and the lie ball r 2 the structure of the operators ti and of the toeplitz c algebra

double positive solutions for a nonlinear four point boundary value problem with a p laplacian operator in this paper we study the existence of positive solutions for a nonlinear four point boundary value problem with a p laplacian operator by using a three functionals fixed point theorem in a cone the existence of double positive solutions for the nonlinear four point boundary value problem with ap laplacian operator is obtained this is different than previous results

on canonical metrics on cartan hartogs domains the cartan hartogs domains are defined as a class of hartogs type domains over irreducible bounded symmetric domains the purpose of this paper is twofold firstly for a cartan hartogs domain omega b d 0 mu endowed with the canonical metric g mu we obtain an explicit formula for the bergman kernel of the weighted hilbert space mathcal h alpha of square integrable holomorphic functions on left omega b d 0 mu g mu right with the weight exp alpha varphi where varphi is a globally defined kahler potential for g mu for alpha 0 and furthermore we give an explicit expression of the rawnsley s varepsilon function expansion for left omega b d 0 mu g mu right secondly using the explicit expression of the rawnsley s varepsilon function expansion we show that the coefficient a 2 of the rawnsley s varepsilon function expansion for the cartan hartogs domain left omega b d 0 mu g mu right is constant on omega b d 0 mu if and only if left omega b d 0 mu g mu right is biholomorphically isometric to the complex hyperbolic space so we give an affirmative answer to a conjecture raised by m zedda

positive solutions for a system of p laplacian boundary value problems this paper is concerned with the existence and multiplicity of positive solutions for the system of p laplacian boundary value problems u i p i 1 f i t u 1 u n u i 0 u i 1 0 i 1 n where n 2 p i 1 f email protected c 0 1 xr n r i 1 n r 0 based on a priori estimates achieved by utilizing the jensen integral inequalities and r n monotone matrices we use fixed point index theory to establish the existence and multiplicity of positive solutions for the above problem

function spaces and reproducing kernels on bounded symmetric domains there are several natural hilbert spaces of holomorphic functions on a bounded symmetric domain such are the bergman type spaces on which the holomorphic discrete series operates and the hardy type spaces which are related to the analytic continuation of the holomorphic discrete series also closely related is the bergmann space of entire functions on the ambient which arises as the closure of the polynomials with respect to a natural inner product the space of holomorphic polynomials decomposes into irreducible subspaces under the action of the isotropy group k of the domain the main facts about this decomposition were proved by schmid 21 for another proof see 22 each irreducible subspace contains a unique normalized l invariant spherical polynomial where l is the isotropy group of the shilov boundary in k our first main result is the explicit computation of the norms of the spherical polynomials with respect to each of the hilbert spaces considered for the domains of classical type they were considered by hua 9 and for some of the hilbert spaces this was done before by upmeier 24 using different methods for certain others there are partial results in 22 we are able to do this in a fairly simple unified way by making strong use of gindikin s generalized gamma function s next we obtain a description of the reproducing kernels of the k irreducible subspaces in each of our hilbert spaces and an expansion in terms of these for

integrals over the circular ensembles relating to classical domains using the theory of classical domains and jack polynomials we generalize several integrals over the unitary group due to fyodorov and khoruzhenko to integrals over the circular orthogonal and circular symplectic ensembles while in the unitary case a fundamental role is played by complex matrices it is anti symmetric and symmetric matrices which play the same role in the latter two cases in our workings a generalization of the evaluation of the integral of a jack polynomial times the selberg weight sought by fyodorov and khoruzhenko is identified

the explicit forms and zeros of the bergman kernel function for hartogs type domains abstract we define the cartan hartogs domain which is the hartogs type domain constructed over the product of bounded hermitian symmetric domains and compute the explicit form of the bergman kernel for the cartan hartogs domain using the virtual bergman kernel as the main contribution of this paper we show that the main part of the explicit form of the bergman kernel is a polynomial whose coefficients are combinations of stirling numbers of the second kind using this observation as an application we give an algorithmic procedure to determine the condition that their bergman kernel functions have zeros

symbols and orbits for 3 step nilpotent lie groups abstract sufficient conditions are derived for l 2 boundedness of a convolution operator on a 3 step nilpotent lie group this is achieved by producing estimates on the kirillov symbol of the operator and is closely linked to the co adjoint orbit structure of the group a structure theorem for 3 step nilpotent lie groups with 1 dimensional center is proved

a quantization of the cartan domain bd i q 2 and operators on the light cone abstract the weyl definition of pseudodifferential operators lends itself in a natural way to generalizations to hermitian symmetric spaces the boundedness of operators obtained in the case of the domain bd i q 2 is proven as a major step towards the development of a symbolic calculus of operators on the light cone

existence of three positive solutions for boundary value problems with p laplacian abstract by using fixed point theorem we study the following equation g u t a t f u 0 subject to boundary conditions where g v v p 2 v with p 1 the existence of at least three positive solutions is proved

existence of three positive pseudo symmetric solutions for a one dimensional p laplacian abstract we apply the five functionals fixed point theorem to verify the existence of at least three positive pseudo symmetric solutions for the three point boundary value problem g u a t f u 0 u 0 0 and u u 1 where g v v p 2 v with p 1 and 0 1

double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale