one parameter groups of regular quasimultipliers abstract groups of unbounded operators are approached in the setting of the esterle quasimultiplier theory we introduce groups of regular quasimultipliers of growth or groups for short where is a continuous weight on the real line we study the relationship of groups with families of operators and homomorphisms such as regularized distribution and integrated groups holomorphic semigroups and functional calculi some convolution banach algebras of functions with derivatives to fractional order are needed which we construct using the weyl fractional calculus

structured populations cell growth and measure valued balance laws abstract a well posedness theory of measure valued solutions to balance laws is presented nonlinear semigroups are constructed by means of the operator splitting algorithm this approach allows to separate the differential terms from the integral ones leading to a significant simplification of the proofs continuous dependence with respect to parameters is also shown the whole framework allows a unified approach to a variety of structured population models providing to each of them the basic well posedness and stability results

oscillatory integrals and lp estimates for schrodinger equations abstract this paper is concerned with schrodinger equations whose principal operators are elliptic under certain degenerate condition we show the estimate of an oscillatory integral related to the solution operator in free case and then employ fractionally integrated groups to obtain the l p estimate of solutions for the initial data belonging to a dense subspace of l p in the case of integrable potentials which improves the corresponding result in m balabane h a emami rad l p estimates for schrodinger evolution equations trans amer math soc 292 1985 357 373

relative entropies for kinetic equations in bounded domains irreversibility stationary solutions uniqueness the relative entropy method describes the irreversibility of the vlasov poisson and vlasov boltzmann poisson systems in bounded domains with incoming boundary conditions uniform in time estimates are deduced from the entropy in some cases these estimates are sufficient to prove the convergence of the solution to a unique stationary solution as time goes to infinity the method is also used to analyse other types of boundary conditions such as mass and energy preserving diffuse reflection boundary conditions and to prove the uniqueness of stationary solutions for some special collision terms

algebra homomorphisms defined via convoluted semigroups and cosine functions abstract transform methods are used to establish algebra homomorphisms related to convoluted semigroups and convoluted cosine functions such families are now basic in the study of the abstract cauchy problem the framework they provide is flexible enough to encompass most of the concepts used up to now to treat cauchy problems of the first and second order in general banach spaces starting with the study of the classical laplace convolution and a cosine convolution along with associated dual transforms natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties these correspond to extensions of the cauchy functional equation for semigroups and the abstract d alembert equation for the case of cosine operator functions the algebra homomorphisms obtained provide a way to prove hille yosida type generation theorems for the operator families under consideration

integrated semigroups and linear partial differential equations with delay abstract we study existence and uniqueness of solutions for linear partial differential equations with delay in l p spaces using an approach of batkai and piazzera and a recent perturbation result for integrated semigroups we apply our result to an equation with delay in the highest order derivatives

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

gaussian bounds for higher order elliptic differential operators with kato type potentials abstract let p d be a nonnegative homogeneous elliptic operator of order 2m with real constant coefficients on r n and v be a suitable real measurable function in this paper we are mainly devoted to establish the gaussian upper bound for schrodinger type semigroup e t h generated by h p d v with kato type perturbing potential v which naturally generalizes the classical result for schrodinger semigroup e t v as v k 2 r n the famous kato potential class our proof significantly depends on the analyticity of the free semigroup e t p d on l 1 r n as a consequence of the gaussian upper bound the l p spectral independence of h is concluded

abstract degenerate cauchy problems in locally convex spaces abstract this paper is concerned with the abstract degenerate cauchy problem dcp d dt bu t au t t 0 bu 0 bu 0 where a and b are closed linear operators in a sequentially complete locally convex space a c propagation family for dcp is introduced c is an operator leading to a general c wellposedness result about dcp moreover conditions are given ensuring the existence of c propagation families for those dcp with differential operators on various function spaces with frechet topologies as coefficient operators these results are new even in the case of banach spaces

generation of the integrated semigroups by superelliptic differential operators abstract let a be a superelliptic differential operator of order 2m introduced by e b davies e b davies uniformly elliptic operators with measurable coefficients j funct anal 132 1995 141 169 in the case of 2 m n he obtained the upper gaussian bound of the integral kernel representing e z a z c and the estimates of the l p operator norm of the semigroup for all p 1 the purpose of the present paper is to show that i a k for some constant k 0 generates an integrated semigroup on l p weighted l p space and l p l q to prove this we need norm estimates of e z a z c on each of these spaces also we get another norm estimate of e z a z c on l p when 2 m n without using the integral kernel this norm estimate is better than that in e b davies uniformly elliptic operators with measurable coefficients j funct anal 132 1995 141 169 and gives a better times of the integration of the integrated semigroup

on duality and spectral properties of a k regularized resolvents we construct a duality theory for a k regularized resolvents extending some of the known theorems for dual semigroups we present several classes of spaces which in the semigroup case correspond to the favard class and the sun dual space by duality arguments spectral inclusions theorems for regularized resolvents are also obtained

the cauchy problem for critical and subcritical semilinear parabolic equations in lr ii initial data in critical sobolev spaces abstract by presenting some time space l p l r estimates we will establish the local and global existence and uniqueness of solutions for semilinear parabolic equations with the cauchy data in critical sobolev spaces of negative indices our results contain the complex derivative ginzburg landau equation and the cahn hilliard equation as special cases

fuzzy pattern recognition based approach to biometric score fusion problem abstract this paper introduces a novel approach for biometric score fusion problem that can be viewed as a fuzzy pattern recognition one in this approach the matching score space is considered as consisting of two fuzzy sets genuine and impostor first each individual matcher is modeled as a fuzzy set using an automatic membership function generation method in order to handle uncertainty and imperfection in matching scores then the new fuzzy matching scores are fused with a fuzzy aggregation operator and the final decision is given experimental results on well known benchmark databases show that our method significantly improves single best biometric matcher performance and reaches comparable results to several relevant methods moreover the proposed method exhibits high robustness to small size of client training data

likelihood ratio based biometric score fusion multibiometric systems fuse information from different sources to compensate for the limitations in performance of individual matchers we propose a framework for the optimal combination of match scores that is based on the likelihood ratio test the distributions of genuine and impostor match scores are modeled as finite gaussian mixture model the proposed fusion approach is general in its ability to handle 1 discrete values in biometric match score distributions 2 arbitrary scales and distributions of match scores 3 correlation between the scores of multiple matchers and 4 sample quality of multiple biometric sources experiments on three multibiometric databases indicate that the proposed fusion framework achieves consistently high performance compared to commonly used score fusion techniques based on score transformation and classification

c0 semigroups on a locally convex space abstract a necessary and sufficient condition that a densely defined linear operator a in a sequentially complete locally convex space x be the infinitesimal generator of a quasi equicontinuous c0 semigroup on x is that there exist a real number 0 such that for each the resolvent i a 1 exists and the family k i a k k 0 1 2 is equicontinuous in this case all resolvents i a 1 of the given operator a and all exponentials exp ta t 0 of the operator a belong to a banach algebra b x which is a subspace of the space l x of all continuous linear operators on x and for each t 0 and for each x x one has limk z i k 1ta k x exp ta x a perturbation theorem for the infinitesimal generator of a quasi equicontinuous c0 semigroup by an operator which is an element of b x is obtained

approximation of local convoluted semigroups abstract we extend the trotter kato theorem on c 0 semigroups to local convoluted semigroups on dual spaces and apply these results to the general banach space setting compared to known results we obtain weaker convergence assumptions on the resolvent

asymptotic behaviour of integrated semigroups abstract in this paper we investigate the asymptotic behaviour of cauchy problems which are not governed by strongly continuous semigroups we obtain interesting generalizations in terms of integrated semigroups of classical abelian and tauberian theorems the results are applied to the solution of the schrodinger equation in l p spaces

estimates for schrodinger evolution equations on demontre que pour des donnees de cauchy dans l 1 r n la solution d une equation d evolution de schrodinger a coefficients constants d ordre 2m est uniformement bornee pour t 0 de borne 1 t c ou c est un entier c n 2m 1

laplace transforms and integrated regularized semigroups in locally convex spaces abstract in this paper we consider the vector valued laplace transforms r times r 0 integrated semigroups and regularized semigroups in the context of sequentially complete locally convex spaces our theorems develop the corresponding results in 1 11 including the well known integrated version of the classical widder s representation theorem of laplace transforms for functions taking values in banach spaces moreover we study a class of differential operators on certain function spaces optimal conditions making them the generators of integrated or regularized semigroups are obtained we finally show some applications to abstract cauchy problems

integrated semigroups and the cauchy problem for systems in lp spaces abstract in this note we prove that under suitable hypotheses every homogeneous differential operator on lp r n n corresponding to a system which is well posed in l2 r n n generates an times integrated semigroup on lp r n n 1 n 1 2 1 p for some special systems of mathematical physics such as the wave equation or maxwell s equations this constant can be improved to be n 1 1 2 1 p

rank 1 perturbations of cosine functions and semigroups abstract let a be the generator of a cosine function on a banach space x in many cases for example if x is a umd space a b generates a cosine function for each b l d a 1 2 x if a is unbounded and 1 2 1 then we show that there exists a rank 1 operator b l d a x such that a b does not generate a cosine function the proof depends on a modification of a baire argument due to desch and schappacher it also allows us to prove the following if a b generates a distribution semigroup for each operator b l d a x of rank 1 then a generates a holomorphic c 0 semigroup if a b generates a c 0 semigroup for each operator b l d a x of rank 1 where 0 1 then the semigroup t generated by a is differentiable and t t o t as t 0 for any 1 this is an approximate converse of a perturbation theorem for this class of semigroups

spectra of pseudodifferential operators generating integrated semigroups consider the lp realization opp a of a pseudodifferential operator with symbol a e sp70 having constant coefficients we show that for a certain class of symbols the spectrum of opp a is independent of p this implies that opp a generates an n times integrated semigroup on lp i rn for a certain n if and only if p opp a 8 0 and the numerical range of a is contained in a left half plane our method allows us also to construct examples of operators generating integrated semigroups on lp rn if and only if p is sufficiently close to 2

schrodinger type evolution equations in lp ω abstract let ap be a strongly elliptic operator of order 2m m n in lp 1 p a bounded domain of rn with dirichlet or neumann boundary conditions of concern is the cauchy problem for schrodinger type evolution equations in lp formula by showing that iap is the generator of a c0 group on a certain interpolation space we obtain results of wellposedness for which are stronger than those derived from the regularized or integrated groups on lp as a by product it is shown that iap is the generator of a ap r regularized group 0 on lp for all formula

optimal control of fractional diffusion equation in this paper we apply the classical control theory to a fractional diffusion equation in a bounded domain the fractional time derivative is considered in a riemann liouville sense we first study the existence and the uniqueness of the solution of the fractional diffusion equation in a hilbert space then we show that the considered optimal control problem has a unique solution interpreting the euler lagrange first order optimality condition with an adjoint problem defined by means of right fractional caputo derivative we obtain an optimality system for the optimal control

integrated semigroups and higher order abstract equations abstract let e be a banach space b 0 b n 1 closed linear operators on e and f 0 e this paper is devoted to the study of well posedness of the cauchy problem for higher order abstract differential equations formula using the theory of integrated semigroups we obtain some concise and useful criteria

lp lq estimates for dispersive equations and related applications abstract this paper is mainly concerned with the l p l q estimates of solutions for a class of general dispersive equations under the condition h b with an index b 0 1 to the end the new pointwise decay estimates of oscillatory integrals related to the fundamental solutions are proved if b 1 then the pointwise estimates are particularly consistent with the sharp results of the nondegenerate cases moreover as an application of the l p l q estimates we also show that higher order differential operator i p d v x d generates a fractionally integrated group on some l p r n from which certain l p estimates for the solutions of generalized schrodinger equations are obtained

the hille yosida and trotter kato theorems for integrated semigroups abstract we completely characterize the generators of non degenerate exponentially bounded n times integrated semigroups we deduce some perturbation results we also give a proof of the trotter kato theorem inspired from the classical one

fuzzy sets in pattern recognition accomplishments and challenges abstract we identify and discuss a role that fuzzy sets play in pattern recognition the main conceptual and algorithmic challenges are outlined highlighted are also some future trends

integrated semigroups and related partial differential equations abstract we investigate the relationship between abstract linear evolution equations of heat wave and schrodinger types in terms of well posedness in banach spaces more precisely we study our operators as generators of integrated semigroups and integrated cosine functions as applications we consider in a banach space context an abstract laplacian which generalizes the ordinary laplacian in thelp r n spaces we obtain optimal results when compared to the classical situation where the generation results were obtained by 17 using completely different methods our main tools are the boundary value theorem for holomorphic semigroups and the abstract weierstrass formula related partial differential equations have been considered previously by bragg and dettman

global weak solutions of vlasov maxwell systems we study here the vlasov maxwell system in its classical and relativistic form we prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data the main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work

a landau kolmogorov inequality for generators of families of bounded operators abstract a landau kolmogorov type inequality for generators of a wide class of strongly continuous families of bounded and linear operators defined on a banach space is shown our approach allows us to recover in a unified way known results about uniformly bounded c 0 semigroups and cosine functions as well as to prove new results for other families of operators in particular if a is the generator of an times integrated family of bounded and linear operators arising from the well posedness of fractional differential equations of order 1 then we prove that the inequality a x 2 8 m 2 2 2 1 2 3 x a 2 x holds for all x d a 2