the hyperbolic class of quadratic time frequency representations i constant q warping the hyperbolic paradigm properties and members the time frequency tf version of the wavelet transform and the affine quadratic bilinear tf representations can be used for a tf analysis with constant q characteristic the paper considers a new approach to constant q tf analysis a specific tf warping transform is applied to cohen s class of quadratic tf representations which results in a new class of quadratic tf representations with constant q characteristic the new class is related to a hyperbolic tf geometry and is thus called the hyperbolic class hc two prominent tf representations previously considered in the literature the bertrand p sub 0 distribution and the altes marinovic q distribution are members of the new hc the authors show that any hyperbolic tf representation is related to both the wideband ambiguity function and a hyperbolic ambiguity function it is also shown that the hc is the class of all quadratic tf representations which are invariant to hyperbolic time shifts and tf scalings operations which are important in the analysis of doppler invariant signals and self similar random processes the paper discusses the definition of the hc via constant q warping some signal theoretic fundamentals of the hyperbolic tf geometry and the description of the hc by 2d kernel functions several members of the hc are considered and a list of desirable properties of hyperbolic tf representations is given together with the associated kernel constraints

multiplicity of single bump solutions for semilinear elliptic equations in multi bump domains abstract in this paper we study the decomposition of the filtration of the nehari manifold via the variation of domain shape furthermore we use this result to prove that the semilinear elliptic equation in the multi bump domain r has multiple positive solutions and we can find at least one ground state solution

normal forms and quadratic nonlinear klein gordon equations on construit une transformation qui change l equation a non linearite cubique que l on sait resoudre a 3 1 dimensions on demontre que la solution du probleme original a le meme comportement asymptotique que l equation de klein gordon non lineaire

three positive solutions of nonhomogeneous semilinear elliptic equations abstract in this paper we use new analyses to assert that there are three positive solutions of eq 1 1 in infinite cylinder domain with hole a d

temps d existence pour l equation de klein gordon semi lineaire a donnees petites periodiques we study lower bounds for the maximal time of existence t of a smooth solution to a semi linear klein gordon equation u u f u u with periodic cauchy data of small size if f vanishes at order r at 0 we prove that t c 2 if r 2 t c r 1 log r 3 if r 3 we construct examples showing the optimality of these results for convenient values of r

multiplicity and concentration of solutions for nonhomogeneous elliptic equations in multi bump domains abstract in this paper we study the decomposition of the filtration of the nehari manifold via the variation of domain shape furthermore we use this result to prove that the nonhomogeneous elliptic equations in an m bump domain have at least m 1 positive solutions

multiplicity of positive solutions for semilinear elliptic problems in unbounded domains in this paper we study the effect of domain shape on the multiplicity of positive solutions for the semilinear elliptic equations we prove a palais smale condition in unbounded domains and assert that the semilinear elliptic equation in unbounded domains has multiple positive solutions

analytical construction and fast computation of frequency warping operators and dual frame frequency warping has been introduced as a unitary operator over a nonfinite domain in practical applications the need of a feasible implementation forces to redefine frequency warping over finite domains in the framework of redundant transformations called frames where the unitary property is replaced by the tight frame property i e the adjoint operator behaves as pseudo inverse in case a tight frame cannot be designed inversion can be achieved by finding the dual frame in this work with reference to nonsmooth warping functions we present a new approach to the construction and fast computation of the dual frame operator based on an operator power series with respect to previous approaches many limitations are overcome while maintaining important properties of frequency warping

multiple positive solutions for semilinear dirichlet problems with sign changing weight function in infinite strip domains abstract in this paper existence and multiplicity results to the following dirichlet problem u u f x u q 1 h x u p 1 in u 0 in u 0 on are established where r r n 1 is bounded smooth domain and n 2 here 1 q 2 p 2 2 2 n n 2 if n 3 2 if n 2 is a positive real parameter the function f among other conditions can possibly change sign in and the function h satisfies suitable conditions the study is based on the comparison of energy levels on nehari manifold

analysis and synthesis of multicomponent signals using positive time frequency distributions a new approach to the analysis and reconstruction of multicomponent nonstationary signals from their time frequency distribution tfd is presented specifically we consider a tfd based on the recently introduced minimum cross entropy principle mce this positive tfd is cross terms free and hence has an advantage over the family of bilinear distributions based on the mce tfd a new algorithm for reconstructing the phase and amplitude parameters of each component of the signal is developed to evaluate the accuracy of the algorithm monte carlo simulations are presented and compared with the corresponding cramer rao bound it is shown that the new algorithm is superior to presently available methods in both efficiency and performance it is concluded that together with the mce tfd representation the proposed approach provides a powerful tool for analysis of nonstationary multicomponent signals embedded in additive gaussian noise

almost global existence for the semi linear klein gordon equation on the circle abstract we show that the solution to the semi linear klein gordon equation on the circle with a nonlinearity satisfying a convenient condition exists almost globally for almost every positive mass provided that it is either even or odd as a function of the space variable we also show that if the nonlinearity is independent of the space derivative of the unknown and if it is also even as a function of the time derivative then the solution exists almost globally for almost every positive mass the results are based on the method of normal forms the difficulty is to find a structure of the nonlinearity so that the process of normal forms can be performed up to any order

existence of positive solutions of some nonlinear elliptic problems in unbounded domains in this paper we study the existence of positive solutions of some nonlinear elliptic problems in unbounded domains the existence is affected by the properties of the geometry and the topology of the domain

long time existence for semi linear klein gordon equations with small cauchy data on zoll manifolds we prove a long time existence result for semi linear klein gordon equations with small cauchy data on zoll manifolds this generalizes a preceding result concerning the case of spheres obtained in an earlier paper by the authors the proof relies on almost orthogonality properties of products of eigenfunctions of positive elliptic selfadjoint operators on a compact manifold and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on zoll manifolds

three positive solutions for nonlinear elliptic equations in finite strip with hole in this paper we study the effect of the domain on the multiplicity of positive solutions for the nonlinear elliptic equation using the ekeland variational principle and the center mass function we prove that there are at least three positive solutions for the nonlinear elliptic equation in finite strip with holes

three positive solutions of semilinear elliptic equations in the half space with a hole abstract in this paper assume that h is nonnegative and h l 2 0 we prove that if h l 2 is sufficiently small then there are at least three positive solutions of eq 1 in r n d where d is a c 1 1 bounded domain in r n

multiple positive solutions for dirichlet problems involving concave and convex nonlinearities abstract in this paper we study the multiplicity of positive solutions for the following dirichlet problems involving concave and convex nonlinearities u u f x u q 2 u h x u p 2 u in a u h 0 1 a where 1 q 2 p 2 2 2 n n 2 if n 3 2 if n 2 0 a r is an infinite strip in r n is a bounded domain in r n 1 and f x h x satisfy suitable conditions

the cauchy problem for non linear klein gordon equations we consider in n 1 n 2 the non linear klein gordon equation we prove for such an equation that there is a neighbourhood of zero in a hilbert space of initial conditions for which the cauchy problem has global solutions and on which there is asymptotic completeness the inverse of the wave operator linearizes the non linear equation if moreover the equation is manifestly poincare covariant then the non linear representation of the poincare lie algebra associated with the non linear klein gordon equation is integrated to a non linear representation of the poincare group on an invariant neighbourhood of zero in the hilbert space this representation is linearized by the inverse of the wave operator the hilbert space is in both cases the closure of the space of the differentiable vectors for the linear representation of the poincare group associated with the klein gordon equation with respect to a norm defined by the representation of the enveloping algebra

unitary equivalence a new twist on signal processing unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time frequency and scale implementation of these new tools involves simply preprocessing the signal by a unitary transformation performing standard processing on the transformed signal and then in some cases transforming the resulting output the resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and hence prove useful for representing and processing signals that are not well matched by current techniques as specific examples of this procedure we generalize linear time invariant systems orthonormal basis and frame decompositions and joint time frequency and time scale distributions these applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature

multiplicity of positive and nodal solutions for semilinear elliptic equations in infinite strips abstract in this paper we study the multiplicity of positive and nodal solutions of the following semilinear elliptic equation u u g x u p 2 u in a u h 0 1 a where 2 p 2 n n 2 n 3 the parameter 0 a r is an infinite strip in r n and is a bounded domain in r n 1 we assume that g x a x b x is a positive function where the functions a and b are satisfying some suitable conditions

multiplicity of nodal solutions for elliptic problems involving non odd nonlinearities abstract in this paper we study the effect of domain shape on the number of 2 nodal solutions for the semilinear elliptic equation involving non odd nonlinearities we prove that a semilinear elliptic equation in an m bump domain possibly unbounded has m 2 2 nodal solutions and we can find a least energy nodal solution in those solutions furthermore we can describe the bump location of these solutions

frequency warping biorthogonal frames frequency warping is theoretically designed to be a unitary operator of infinite input and output dimensions thus performing the resolution of identity in real implementations finite dimensions have to be considered then perfect reconstruction cannot be fulfilled the accuracy of reconstruction is particularly compromised in case of non smooth warping maps which are more useful for practical applications in order to overcome this limitation a new frequency warping biorthogonal frame operator for non smooth warping maps is introduced in this work the proposed transformation is based on a mathematical model which has been previously introduced for computational purposes by adding some redundancy with respect to the truncation of the infinite dimensions operator the effect of an infinite output dimension can be taken into account in a compressed way based on an analytical factorization in the reconstruction process the additional redundant samples are expanded thus guaranteeing near perfect reconstruction

symmetry of positive solutions of semilinear elliptic equations in infinite strip domains abstract in this article we apply the improved moving plane method to prove the symmetry of the solutions of the dirichlet problem u u g u in infinite strip domains with zero boundary condition

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

almost global existence for hamiltonian semilinear klein gordon equations with small cauchy data on zoll manifolds this paper is devoted to the proof of almost global existence results for klein gordon equations on zoll manifolds e g spheres of arbitrary dimension with hamiltonian nonlinearities when the cauchy data are smooth and small the proof relies on birkhoff normal form methods and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on zoll manifolds 2007 wiley periodicals inc

fast computation of frequency warping transforms in this paper we introduce an analytical approach for the frequency warping transform criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined such operators can be used to shape the tiling of time frequency tf plane in a flexible way moreover they are designed to be inverted by the application of their adjoint operator according to the proposed model the frequency warping transform is computed by considering two additive operators the first one represents its nonuniform fourier transform approximation and the second one suppresses aliasing the first operator is fast computable by various interpolation approaches a factorization of the second operator is found for arbitrary shaped nonsmooth warping maps by properly truncating the operators involved in the factorization the computation turns out to be fast without compromising accuracy

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

fast fourier transforms for nonequispaced data a group of algorithms is presented generalizing the fast fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval pi pi the schemes of this paper are based on a combination of certain analytical considerations with the classical fast fourier transform and generalize both the forward and backward ffts each of the algorithms requires o n cdot log n n cdot log 1 varepsilon arithmetic operations where varepsilon is the precision of computations and n is the number of nodes the efficiency of the approach is illustrated by several numerical examples

existence of positive solutions for some nonlinear elliptic equations on unbounded domains with cylindrical ends abstract in this paper we study the existence of positive solutions to nonlinear elliptic boundary value problems on unbounded domains r n with cylindrical ends for a general nonlinear term f u including f u u p 1 n 2 as a typical example u u f u u 0 x u 0 u x 0 x by using the mountain pass approach the geometry of plays an important role in our analysis

long time sobolev stability for small solutions of quasi linear klein gordon equations on the circle we prove that higher sobolev norms of solutions of quasi linear klein gordon equations with small cauchy data on s 1 remain small over intervals of time longer than the ones given by local existence theory this result extends previous ones obtained by several authors in the semi linear case the main new difficulty one has to cope with is the loss of one derivative coming from the quasi linear character of the problem the main tool used to overcome it is a global paradifferential calculus adapted to the sturm liouville operator with periodic boundary conditions