holomorphic extensions of representations i automorphic functions let g be a connected real semisimple lie group contained in its complexification gc and let k be a maximal compact subgroup of g we construct a kc g double coset domain in gc and we show that the action of g on the k finite vectors of any irreducible unitary representation of g has a holomorphic extension to this domain for the resultant holomorphic extension of k finite matrix coefficients we obtain estimates of the singularities at the boundary as well as majorant minorant estimates along the boundary we obtain l bounds on holomorphically extended automorphic functions on g k in terms of sobolev norms and we use these to estimate the fourier coefficients of combinations of automorphic functions in a number of cases e g of triple products of maas forms

stochastic uncertain systems subject to relative entropy constraints induced norms and monotonicity properties of minimax games entropy and relative entropy are fundamental concepts on which information theory is founded on and in general telecommunication systems design on the other hand dissipation inequalities minimax strategies and induced norms are the basic concepts on which robustness of uncertain control and estimation of systems are founded on in this paper the precise relation between these notions is investigated in particular it will be shown that the higher the dissipation the higher the entropy of the system which has implications in computing the induced norm associated with robustness these connections are obtained by considering stochastic optimal uncertain control systems in which uncertainty is described by a relative entropy constraint between the nominal and uncertain measures while the pay off is a linear functional of the uncertain measure this is a minimax game in which the controller measure seeks to minimize the pay off while the disturbance measure aims at maximizing the pay off salient properties of the minimax solution are derived including a characterization of the optimal sensitivity reduction computation of the induced norm monotonicity properties of minimax solution and relations between dissipation and relative entropy of the system the theory is developed in an abstract setting and then applied to nonlinear partially observable continuous time uncertain controlled systems in which the nominal and uncertain systems are described by conditional distributions in addition existence of the optimal control policy among the class of policies known as wide sense control laws is shown and an explicit formulae for the worst case conditional measure is derived the results are applied to linear quadratic gaussian problems

the segal bargmann coherent state transform for compact lie groups abstract let k be an arbitrary compact connected lie group we describe on k an analog of the segal bargmann coherent state transform and we prove theorem 1 that this generalized coherent state transform maps l 2 k isometrically onto the space of holomorphic functions in l 2 g where g is the complexification of k and where is an appropriate heat kernel measure on g the generalized coherent state transform is defined in terms of the heat kernel on the compact group k and its analytic continuation to the complex group g we also define a k averaged version of the coherent state transform and we prove a similar result for it theorem 2 in the appendix we describe the coherent states which motivate the definitions of these transforms in section 9 we obtain inversion formulas for both the coherent state transform and the k averaged coherent state transform theorems 3 4 as a consequence we obtain formulas for certain bergman kernels on the complex group g theorems 5 6 in section 10 we derive a general paley wiener theorem for k and we exhibit a family of convolution transforms each of which is an isometric isomorphism of l 2 k onto a certain l 2 space of holomorphic functions on g these transforms include the k averaged coherent state transform as a special case we also discuss the analogous results for r 1 the results of section 10 are theorems 7 10 finally in section 11 we discuss the case of quotient spaces we prove theorem 11 that both the coherent state transform and the k averaged coherent state transform pass in a natural way from k to k h where h is a closed connected subgroup of k

variational processes from the weak forward equation in this paper the author constructs markov diffusion processes from a given system of borel probability measures on ad dimensional euclidean space he constructs a so called variational process which does not always coincide with a nelson process he also discusses schrodinger s problem in quantum mechanics

the inverse segal bargmann transform for compact lie groups in this paper i give a new inversion formula theorem 1 for the generalized segal bargmann transform introduced in b c hall j funct anal 122 1994 103 151 the inversion formula may be viewed as a formula for theinverseheat operator for a compact lie group i then use this formula to give a new direct proof of the unitary of thek invariant form of the segal bargmann transform theorem 2 the proof of the inversion formula relies on an identity theorem 5 which relates the laplacian for a compact lie groupkto the laplacian for the non compact dual symmetric space kc k

on π quasinormally embedded subgroups of finite group a subgroup of a group g is said to be quasinormal in g if it permutes with every sylow subgroup of g a subgroup h of a group g is said to be quasinormally embedded in g if for each prime dividing the order of h a sylow p subgroup of h is also a sylow p subgroup of some quasinormal subgroups of g in this paper we investigate the influence of quasinormally embedded of maximal or minimal subgroup of sylow subgroups of the generalized fitting subgroup of a finite group the main theorems are as follows theorem 1 1 let f be a saturated formation containing u suppose that g is a group then g f if and only if there is a normal subgroup h of g such that g h f and all maximal subgroups of any sylow subgroup of f h are quasinormally embedded in g theorem 1 2 let f be a saturated formation containing u and let g be a group then g f if and only if there is a normal subgroup h in g such that g h f and the subgroups of prime order or order 4 of the generalized fitting subgroup f h are quasinormally embedded in g theorem 1 3 let f be a saturated formation such that n f let g be a group such that every element of order 4 of the generalized fitting subgroup f gf is quasinormally embedded in g then g belongs to f if and only if x lies in the f hypercenter zf g of g for every element x of prime order of f gf these results extended recent results of asaad et al on s quasinormally embedded subgroups of finite groups j pure appl algebra 165 2001 129 135 li et al the influence of minimal subgroups on the structure of finite groups proc amer math soc in press the influence of quasinormality of maximal subgroups of sylow subgroups of a finite group arch math in press

state distributions and minimum relative entropy noise sequences in uncertain stochastic systems the discrete time case this paper is concerned with dissipativity theory and robust performance analysis and design of discrete time stochastic systems driven by statistically uncertain random noise the uncertainty is quantified by the conditional relative entropy of the actual probability law of the noise with respect to a nominal product measure corresponding to a white noise sequence we discuss a balance equation dissipation inequality and superadditivity property for the corresponding conditional relative entropy supply as a function of time the problem of minimizing the supply required to drive the system between given state distributions over a specified time horizon is considered such variational problems involving entropy and probabilistic boundary conditions are known in the literature as schrodinger bridge problems in application to control systems the minimum required conditional relative entropy supply characterizes the robustness of the system with respect to a statistically uncertain random noise we o

an inversion formula for the segal bargmann transform on a symmetric space of non compact type abstract we prove analogs of the heat kernel transform inversion formulae of golse leichtnam and the author e leichtnam f golse m stenzel intrinsic microlocal analysis and inversion formulae for the heat equation on compact real analytic riemannian manifolds ann sci ecole norm sup 4 29 6 1996 669 736 mr1422988 97h 58153 theorems 0 3 0 4 in the setting of a riemannian symmetric space of helgason s non compact type

on the relative entropy of discrete time markov processes with given end point densities given a markov process x k defined over a finite interval i 0 n i spl sub z we construct a process x k with the same initial density as x but a different end point density which minimizes the relative entropy of x and x it is shown that x is a markov process in the same reciprocal class as x in the gaussian case the minimum relative entropy problem is related to a minimum energy lqg optimal control problem

on the geometry of maximum entropy problems we show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite dimensional maximum entropy problems concerning probability distributions spectral densities and covariance matrices these include burg s spectral estimation method and dempster s covariance completion as well as various recent generalizations of the above we then apply this orthogonality principle to the new problem of completing a block circulant covariance matrix when an a priori estimate is available

anisotropy based performance analysis of linear discrete time invariant control systems the anisotropic norm of a linear discrete time invariant system measures system output sensitivity to stationary gaussian input disturbances of bounded mean anisotropy mean anisotropy characterizes the degree of predictability or colouredness and spatial non roundness of the noise the anisotropic norm falls between the h 2 and h infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known this paper develops a method for numerical computation of the anisotropic norm which involves linked riccati and lyapunov equations and an associated special type equation

minimax lqg control of stochastic partially observed uncertain systems we consider an infinite horizon linear quadratic minimax optimal control problem for stochastic uncertain systems with output measurement a new description of stochastic uncertainty is introduced using a relative entropy constraint for the stochastic uncertain system under consideration a connection between the worst case control design problem and a specially parametrized risk sensitive stochastic control problem is established using this connection a minimax optimal lqg controller is constructed which is based on a pair of algebraic matrix riccati equations arising in risk sensitive control it is shown that this minimax optimal controller absolutely stabilizes the stochastic uncertain system

finite groups with generalized ore supplement conditions for primary subgroups abstract we associate with every group g a set g of subgroups of g with 1 g if h g then we say that h is a subgroup of g if g g for each epimorphism g g then we say that is a subgroup functor we say also that a subgroup functor is hereditary provided h e whenever h e g and h g regular provided for any group g whenever h g is a p group and n is a minimal normal subgroup of g then g n g h n is a power of p regular respectively quasiregular provided for any primitive group g whenever h g is a p group and n is a respectively abelian minimal normal subgroup of g then g n g h n is a power of p let k h be subgroups of g and a subgroup functor then we say that the pair k h satisfies the f supplement condition in g if g has a subgroup t such that h t g and h t k z f t h is f supplemented in g if for some subgroup s of g contained in h the pair s h satisfies the f supplement condition in g where g g h g and h h h g in this paper we study the structure of a group g under the condition that some primary subgroups of g are f supplemented in g in particular we prove the following result theorem a let f be a saturated formation containing the class u of all supersoluble groups e a normal subgroup of g with g e f x e or x f e and a regular or hereditary regular subgroup functor suppose that every subgroup of g contained in x is subnormally embedded in g if every maximal subgroup of every non cyclic sylow subgroup of x is u supplemented in g then g f moreover in the case when is regular then every chief factor of g below e is cyclic the results in this paper not only cover and unify a long list of some known results but also cause a wide series of new results

the segal bargmann transform on a symmetric space of compact type abstract we study the segal bargmann transform on a symmetric space x of compact type mapping l 2 x into holomorphic functions on the complexification x c we invert this transform by integrating against a dual heat kernel measure in the fibers of a natural fibration of x c over x we prove that the segal bargmann transform is an isometry from l 2 x onto the space of holomorphic functions on x c which are square integrable with respect to a natural measure these results extend those of b hall in the compact group case

isometry theorem for the segal bargmann transform on a noncompact symmetric space of the complex type we consider the segal bargmann transform on a noncompact symmetric space of the complex type we establish isometry and surjectivity theorems for the transform in a form as parallel as possible to the results in the dual compact case the isometry theorem involves integration over a tube of radius r in the complexification followed by analytic continuation with respect to r a cancellation of singularities allows the relevant integral to have a nonsingular extension to large r even though the function being integrated has singularities

on fφ hypercentral subgroups of finite groups let g be a finite group we write r g to denote the largest soluble normal subgroup of g and put g r g we say that a chief factor h k of g is non frattini non solubly frattini if h k g k if h k g k respectively a chief factor h k of g is called f central in g provided h k g cg h k f a normal subgroup n of g is said to be f hypercentral f hypercentral in g if either n 1 or n 1 and there exists a chief series 1 n0 n1 nt n of g below n such that every non frattini non solubly frattini respectively factor ni ni 1 of series is f central in g in this paper we analyze some properties and applications of f hypercentral and f hypercentral subgroups

on upper estimate of anisotropic norm of uncertain system with application to stochastic robust control abstractthis paper considers a stable linear discrete time invariant system with linear fractional norm bounded uncertainty an estimate of the anisotropic norm of this system is derived it is shown that the anisotropic norm is bounded above if a system of inequalities of certain kind is solvable this system consists of two linear matrix inequalities and inequality with respect to the determinant of a positive definite matrix by minimising the squared threshold value under constraints in form of the system of matrix inequalities one can obtain the upper estimate of the anisotropic norm of the considered system the introduced analysis result is directly applied to solve the problem of synthesis of state feedback robust anisotropic controller

the segal bargmann transform for noncompact symmetric spaces of the complex type we consider the generalized segal bargmann transform defined in terms of the heat operator for a noncompact symmetric space of the complex type for radial functions we show that the segal bargmann transform is a unitary map onto a certain l 2 space of meromorphic functions for general functions we give an inversion formula for the segal bargmann transform involving integration against an unwrapped version of the heat kernel for the dual compact symmetric space both results involve delicate cancellations of singularities

state space formulae for discrete time h optimization abstract state space formulae and proofs are given for ail the important steps in discrete time h 8 optimization the steps closely follow the algorithms for continuous time systems but there are some technically involved differences in the detail that make their derivation non trivial