implicit finite difference approximation for time fractional diffusion equations time fractional diffusion equations are used when attempting to describe transport processes with long memory where the rate of diffusion is inconsistent with the classical brownian motion model in this paper we develop an implicit unconditionally stable numerical method to solve the one dimensional linear time fractional diffusion equation formulated with caputo s fractional derivative on a finite slab several numerical examples of interest are also included

unconditionally convergent l1 galerkin fems for nonlinear time fractional schrodinger equations in this paper a linearized l1 galerkin finite element method is proposed to solve the multidimensional nonlinear time fractional schrodinger equation in terms of a temporal spatial error splitting argument we prove that the finite element approximations in the l 2 norm and l infty norm are bounded without any time step size conditions more importantly by using a discrete fractional gronwall type inequality optimal error estimates of the numerical schemes are obtained unconditionally while the classical analysis for multidimensional nonlinear fractional problems always required certain time step restrictions dependent on the spatial mesh size numerical examples are given to illustrate our theoretical results

fonctions orbitales surgc gr formule d inversion des integrales orbitales et formule de plancherel resume soitgun groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soithune forme reelle degd algebre de lie h apres une etude generale des fonctions orbitales surg h nous construisons des series de fonctions orbitales propres sous l action de l algebre des operateurs differentielsg invariant surg h en utilisant les resultats de p harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication concernant les fonctions generalisees spheriques surg h nous demontrons la formule d inversion des integrales orbitales d une fonction de classec a support compact surg h nous en deduisons la formule de plancherel pour l espace symetriqueg h letgbe a complex connected and simply connected semisimple lie group with lie algebra g lethbe a real form ofgwith lie algebra h after a general study of orbital functions ong h we construct series of orbital functions which are eigen for the action ofg invariant differential operators ong h using the results harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication about spherical generalized functions ong h we prove the inversion formula for orbital integrals of ac function with compact support ong h we deduce the plancherel formula for the symmetric spaceg h

identifying an unknown source in time fractional diffusion equation by a truncation method in this paper an inverse source problem for the time fractional diffusion equation is investigated we prove a conditional stability for this problem a truncation method is presented to deal with the ill posedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter numerical examples show that the proposed method is effective and stable

determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time abstract we consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given the problem considered is one dimensional and the unknown heat source is supposed to be space dependent only the existence and uniqueness results are proved

the dimensions of spaces of holomorphic second order automorphic forms and their cohomology in this paper we answer a question of zagier and find the dimensions of spaces of holomorphic second order forms of even weight we also establish a cohomological interpretation and prove an eichler shimura type isomorphism

base de la serie la plus continue de fonctions generalisees spheriques surgc gr resume soit g un groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soit h une forme reelle de g d algebre de lie h on suppose que h admet une sous algebre de cartan de type compact t pour un element regulier du dual de t on construit une base de l espace des fonctions generalisees spheriques sur g h propres sous l action de l algebre des operateurs differentiels g invariants sur g h pour le caractere defini par on etudie ensuite le prolongement meromorphe en et la croissance des elements de cette base ces fonctions generalisees sont ensuite exprimees en terme de coefficients de representations de g ces resultats sont generalises a d autres series de fonctions generalisees spheriques let g be a complex connected and simply connected semisimple lie group with lie algebra g let h be a real form of g with lie algebra h we suppose that h admits a cartan subalgebra t of compact type for a regular element of the dual of h we construct a basis of the space of spherical generalized functions f such that for all g invariant differential operator d on g h we have d f d f where is the character defined by then we study the meromorphic continuation and the growth of the element of this basis we give these functions in terms of coefficients of representations of g these results are generalized to other series of spherical generalized functions

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

integrales orbitales tordues sur les groupes de lie reductifs reels resume in this article we study orbital integrals on non connected real reductive groups we obtain a characterisation of these functions we construct a family of invariant eigendistributions and we use it to prove an invariant paley wiener theorem

spectral regularization method for a cauchy problem of the time fractional advection dispersion equation in this paper a cauchy problem for the time fractional advection dispersion equation tfade is investigated such a problem is obtained from the classical advection dispersion equation by replacing the first order time derivative by the caputo fractional derivative of order a 0 a 1 we show that the cauchy problem of tfade is severely ill posed and further apply a spectral regularization method to solve it based on the solution given by the fourier method the convergence estimate is obtained under a priori bound assumptions for the exact solution numerical examples are given to show the effectiveness of the proposed numerical method

une correspondance de jacquet langlands p adique we extend the jacquet langlands correspondence between the hecke modules of usual and quaternionic modular forms to overconvergent p adic forms of finite slope we show that this correspondence respects p adic families and is induced by an isomorphism between some associated eigencurves

a space time spectral method for the time fractional diffusion equation in this paper we consider the numerical solution of the time fractional diffusion equation essentially the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term in the former case the first order time derivative is replaced by a fractional derivative making the problem global in time we propose a spectral method in both temporal and spatial discretizations for this equation the convergence of the method is proven by providing a priori error estimate numerical tests are carried out to confirm the theoretical results thanks to the spectral accuracy in both space and time of the proposed method the storage requirement due to the global time dependence can be considerably relaxed and therefore calculation of the long time solution becomes possible

some uniqueness and existence results for the initial boundary value problems for the generalized time fractional diffusion equation in this paper some uniqueness and existence results for the solutions of the initial boundary value problems for the generalized time fractional diffusion equation over an open bounded domain gx 0 t email protected r n are given to establish the uniqueness of the solution a maximum principle for the generalized time fractional diffusion equation is used in turn the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is considered in the paper too another important consequence of the maximum principle is the continuous dependence of the solution on the problem data to show the existence of the solution the fourier method of the variable separation is used to construct a formal solution under certain conditions the formal solution is shown to be a generalized solution of the initial boundary value problem for the generalized time fractional diffusion equation that turns out to be a classical solution under some additional conditions

intertwining operators and residues i weighted characters operateurs d entrelacement normalisation groupes reels groupes p adiques representations standard les distributions j m la distribution j m x residus changements de contour les espaces 7b h ac g f s et 7b f ac g f s l application m

formule d inversion des integrales orbitales tordues sur les groupes de lie reductifs reels resume we continue our study of twisted orbital integrals on real reductive groups in this paper we obtain an inversion formula in the spirit of bouaziz formula for the nontwisted case the distributions given by twisted orbital integrals are decomposed in terms of twisted characters of tempered representations

identifying an unknown time dependent boundary source in time fractional diffusion equation with a non local boundary condition abstract this paper is devoted to determining a time dependent factor of an unknown source on some subboundary conditions for a time fractional diffusion equation from the non local measurement data we prove existence and uniqueness of the solution of the inverse boundary source by using the lax milgram lemma in some suitable sobolev spaces consequently we use the profitable meshless method based on radial basis functions to solve the inverse problem the numerical experimental results and numerical simulations show that the proposed scheme is effective and stable when one considers measurements input data contaminated with noise

a nonlinear parabolic integro differential problem with an unknown dirichlet boundary condition a nonlinear parabolic integro differential equation t g u u f 0 t f s u s d s with a known neumann boundary condition on a part of the boundary and an unknown dirichlet boundary condition t on the other part of the boundary is studied the inverse problem of identifying the unknown time dependent function t from an additional integral measurement e t g u t x d x is investigated the well posedness of the problem in suitable function spaces is shown and a numerical time discrete scheme for approximations is designed convergence of the proposed scheme is supported by a numerical experiment

the method of approximate particular solutions for the time fractional diffusion equation with a non local boundary condition in this paper we consider the numerical solution of the time fractional diffusion equation with a non local boundary condition the method of approximate particular solutions maps using multiquadric radial basis function mq rbf is employed for this equation due to the accuracy of the mq based meshless methods is severely influenced by the shape parameter we adopt a leave one out cross validation loocv algorithm proposed by rippa 34 to enhance the performance of the maps the numerical results obtained show that the proposed numerical algorithm is accurate and computationally efficient for solving time fractional diffusion equation with a non local boundary condition

trace paley wiener theorem in the twisted case a version of the trace paley wiener theorem for a reductive padic group in the context of twisted harmonic analysis with respect to an outer automorphism is proved let g be a connected reductive algebraic group over a p adic field f of characteristic 0 and let g g f let po be a minimal parablic subgroup of g let e be an outer automorphism of g of finite order r of g and suppose that e fixes po elements x y e g are called e conjugate if y g 1xe g for some g e g a distribution on g which is invariant under twisted conjugacy is called e invariant the objects of study in twisted harmonic analysis are e invariant distributions the main examples are provided by twisted orbital integrals invariant integrals over twisted conjugacy classes and by twisted characters which are obtained as follows let ir be an irreducible admissible representation of g and let e 7r denote the representation of g through which g e g acts by r e 1 g if 7r is equivalent to e ir then there exists an operator 7r e unique up to rth roots of unity such that 7r e 7r g 7r e 1 7r e g and ir e r 1 in other words 7r extends to the semidirect product g c x e the twisted character of ir which depends on the choice of ir e is the distribution f tr ir f ir e on the space 1 g of compactly supported locally constant functions on g in applications of the trace formula to global problems in the theory of automorphic representations it is often necessary to use results on the representation theory and harmonic analysis of reductive groups over p adic fields because of the role played by twisted local harmonic analysis in applications of the twisted trace formula e g 1 10 it is important to have available extensions to the twisted case of results known for ordinary harmonic analysis many results in harmonic analysis extend to the twisted case for example by 7 harish chandra s theorem on the local integrability of characters holds for twisted characters the purpose of this paper is to prove a twisted version proposition 11 2 of the trace paley wiener theorem for p adic groups of bernstein deligne and kazhdan given in 3 the twisted paley wiener theorem gives a characterization of functions of the form ir tr ir f i e for some f e g in 1 6 the appropriate setting for the twisted theorem is developed in 710 results needed for the proof of proposition 11 2 are proved propositioii 7 4 is a twisted version of casselman s theorem on characters the proof of proposition 11 2 follows the plan of the argument given in 3 with modifications for the twisted received by the editors december 12 1986 and in revised form june 11 1987 1980 mathematics subject classification 1985 revision primary 22e50 the author was partially supported by grants from the national science foundation and the sloan foundation e 1988 american mathematical society 0002 9947 88 1 00 25 per page

eigenvarieties for reductive groups we develop the theory of overconvergent cohomology introduced by g stevens and we use it to give a construction of eigenvarieties associated to any reductive group g over q such that g r has discrete series we prove that the so called eigenvarieties are equidimensional and generically at over the weight space

a twisted invariant paley wiener theorem for real reductive groups let g be the group of real points of a possibly disconnected linear reductive algebraic group defined over r which is generated by the real points of a connected component g let k be a maximal compact subgroup of the group of real points of the identity component of this algebraic group we characterize the space of maps 7 tr f where is an irreducible tempered representation of g and f varies over the space of smooth compactly supported functions on g which are leftand right k finite this work is motivated by applications to the twisted arthur selberg trace formula

the l2 lefschetz numbers of hecke operators introduction 5 1 hecke operators and l2 cohomology 52 the spectral decomposition of cohomology 6 3 application of the trace formula 54 the functions pa t 5 5 proof of theorem 5 1 6 the main formula appendix bibliography