elliptic boundary value problems with λ dependent boundary conditions abstract in this paper second order elliptic boundary value problems on bounded domains r n with boundary conditions on depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework for a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization procedure in the special case of rational nevanlinna or riesz herglotz functions on the boundary the solution operator is obtained in an explicit form in the product hilbert space l 2 l 2 m which is a natural generalization of known results on linear elliptic boundary value problems and rational boundary value problems for ordinary second order differential equations

odd dimensional orthogonal groups as amalgams of unitary groups part 1 general simple connectedness we extend the phan theory described in c bennett r gramlich c hoffman s shpectorov curtis phan tits theory in a a ivanov m w liebeck j saxl eds groups combinatorics and geometry world scientific river edge 2003 pp 13 29 to the last remaining infinite series of classical chevalley groups over finite fields namely we prove that the twin buildings for the group spin 2n 1 q2 q odd admit a unique unitary flip and that the corresponding flipflop geometry is simply connected for almost all finite fields fq2 applying standard methods from amalgam theory this results in a characterization of central quotients of the group spin 2n 1 q by a phan system of rank one and rank two subgroups in the present first part of a series of two articles we present simple connectedness results for sufficiently large fields or sufficiently large rank to be precise the result stated in the present paper is proved for all cases but n 3 and q 3 5 7 9 the remaining cases are dealt with in the sequel r gramlich m horn w nickel odd dimensional orthogonal groups as amalgams of unitary groups part 2 machine computations submitted for publication computationally

bilinear forms clifford algebras q commutation relations and quantum groups abstract constructions are described which associate algebras to arbitrary bilinear forms generalising the usual clifford and heisenberg algebras quantum groups of symmetries are discussed both as deformed enveloping algebras and as quantised function spaces a classification of the equivalence classes of bilinear forms is also given

lattice chain models for affine buildings of classical type a concrete lattice chain model for the buildings of the classical groups over non archimedean complete skew fields is given the building axioms are proved in a uniform way using hereditary orders with involution instead of lattice chains

extended hilbert space approach to few body problems a general formulation of the quantum scattering theory for a system of few particles which have an internal structure is given due to freezing out the internal degrees of freedom in the external channels a certain class of energy dependent potentials is generated by means of potential theory a modified faddeev equation is derived both in external and internal channels the fredholmity of these equations is proven and this is what provides a sound basis for solving the addressed scattering problem

an addendum to krein s formula abstract we provide additional results in connection with krein s formula which describes the resolvent difference of two self adjoint extensionsa1anda2of a densely defined closed symmetric linear operator with deficiency indices n n n n in particular we explicitly derive the linear fractional transformation relating the operator valued weyl titchmarshm functionsm1 z andm2 z corresponding toa1anda2

weakly closed unipotent subgroups in chevalley groups abstract the goal of this note is to classify the weakly closed unipotent subgroups in the split chevalley groups in an application we show under some mild assumptions on the characteristic that the lie algebra of a connected simple algebraic group fails to be a so called 2f module

on krein s formula in the case of non densely defined symmetric operators abstract in this paper we provide some additional results related to krein s resolvent formula for a non densely defined symmetric operator we show that coefficients in krein s formula can be expressed in terms of analogues of the classical von neumann formulas the relationship between two weyl tichmarsh m functions corresponding to self adjoint extensions of a non densely defined symmetric operator is established

the restricted grassmannian banach lie poisson spaces and coadjoint orbits we investigate some basic questions concerning the relationship between the restricted grassmannian and the theory of banach lie poisson spaces by using universal central extensions of lie algebras we find that the restricted grassmannian is symplectomorphic to symplectic leaves in certain banach lie poisson spaces and the underlying banach space can be chosen to be even a hilbert space smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established several pathological properties of the restricted algebra are pointed out

removal of the resolvent like energy dependence from interactions and invariant subspaces of a total hamiltonian the spectral problem a v z z is considered where the main hamiltonian a is a self adjoint operator of sufficiently arbitrary nature the perturbation v z b a z 1b depends on the energy z as resolvent of another self adjoint operator a the latter is usually interpreted as a hamiltonian describing an internal structure of physical system the operator b is assumed to have a finite hilbert schmidt norm the conditions are formulated when one can replace the perturbation v z with an energy independent potential w such that the hamiltonian h a w has the same spectrum more exactly a part of spectrum and the same eigenfunctions as the initial spectral problem the hamiltonian h is constructed as a solution of the non linear operator equation h a v h it is established that this equation is closely connected with the problem of searching for invariant subspaces of the hamiltonian h b aa b the orthogonality and expansion theorems are proved for eigenfunction systems of the hamiltonian h a w

on groups with root system of type g2 abstract let be a root system of type g 2 and let g be a group generated by non trivial subgroups a satisfying some generalized steinberg relations which are also satisfied by root subgroups corresponding to a moufang hexagon these relations can be considered as a generalization of the element wise commutator relations in chevalley groups the steinberg presentation specifies the groups satisfying the chevalley commutator relations in the present paper some sort of generalized steinberg presentation for groups with root system of type g 2 is provided as a main result we classify the possible structures for g

overgroup lattices in finite groups of lie type containing a parabolic the main theorem is a step in a program to show there exist finite lattices that are not an interval in the lattice of subgroups of any finite group as part of the proof of the main theorem we prove a theorem on the structure of maximal parabolics in finite groups of lie type which is of independent interest

curtis tits groups generalizing kac moody groups of type a n 1 abstract in 13 we define a curtis tits group as a certain generalization of a kac moody group we distinguish between orientable and non orientable curtis tits groups and identify all orientable curtis tits groups as kac moody groups associated to twin buildings in the present paper we construct all orientable as well as non orientable curtis tits groups with diagram a n 1 n 4 over a field k of size at least 4 the resulting groups are quite interesting in their own right the orientable ones are related to drinfeld s construction of vector bundles over a non commutative projective line and to the classical groups over cyclic algebras the non orientable ones are related to expander graphs 14 and have symplectic orthogonal and unitary groups as quotients

complete second order linear differential operator equations in hilbert space and applications in hydrodynamics we study the cauchy problem for a complete second order linear differential operator equation in a hilbert space h of the form d 2 u dt 2 f ik du dt bu f u 0 u 0 u 1 0 u 1 problems of this kind arise e g in hydrodynamics where the coefficients f k and b are unbounded selfadjoint operators it is assumed that f is the dominating operator in the cauchy problem above i e d f d b d f d k we also suppose that f and b are bounded from below but the operator coefficients are not assumed to commute the main results concern the existence of strong solutions to the stated cauchy problem and applications of these results to the cauchy problem associated with small motions of some hydrodynamical systems

spatial antialias filtering in the slowness frequency domain a rigorous explicit spatial antialias filter is designed and applied to spatially coarsely sampled seismic data by removing all energy above the first nyquist wavenumber and aliased energy that is folded back across the nyquist in the horizontal slowness frequency domain the spatial filtering in the slowness frequency domain is explicit free from any event linearity assumption and does not require any interpolation the spatially aliased energy is dispersive and present at small and large slownesses comparison of the output data after antialias spatial filtering with output data after conventional antialias frequency filtering shows that the filter removes the spatially aliased frequencies selectively at each slowness antialias low pass frequency filtering under or overcorrects for spatial aliasing at all slownesses a seismic gather can be spatially dealiased only at the expense of wavelet spectral changes dealiasing and preservation of amplitude variations with offset are not simultaneously possible

sampling aliasing and inverting the linear radon transform sampling a signal too slowly results in temporal frequency aliasing sampling a wave too infrequently in space causes spatial aliasing slowness aliasing is another problem that can occur in some cases even when temporal and spatial frequency aliasing are absent as its name suggests slowness aliasing can cause a wave with one value of slowness to be interpreted as a wave with a different value of slowness for a 2d signal or an image the penalty of undersampling is that we may misrepresent both the spatial frequency and the orientation of the pattern if the pattern is moving then the direction of motion may also be misrepresented the linear radon transform deans 1983 or the related slope intercept form durrani and bisset 1984 is a useful tool to analyze seismic data foster and mosher 1992 dunne and beresford 1995 although sampling and aliasing are two recurring problems turner 1990 marfurt et al 1996 bardan 1998 on the other hand in the optical literature fowles 1989 the effect of fraunhofer diffraction indicates what is happening when a grating is illuminated by a monochromatic plane wave this paper demonstrates how sampling and inverting of the linear radon transform is related to fraunhofer diffraction patterns

complete reducibility of quadratic modules for finite lie type groups let g be a finite lie type group in char p 3 different from sl2 3 and v a zpg module on which the root groups of g act quadratically i e v ar ar 0 for all roots of the root system of g then we show that v is completely reducible

wavelet radon domain dealiasing and interpolation of seismic data spatial aliasing is unavoidable in some seismic data and has serious effects on the performance of multichannel data processing and migration antialias filtering produces distortion of the signal through the removal of high frequency information in contrast dealiasing produces an unaliased estimate of the signal at all frequencies present in the original time series a new dealiasing algorithm is developed by exploiting the properties of seismic wavefields in the wavelet radon transform domain specifically the overlap of information between wavelet scales at the same frequency the effectiveness of the wavelet radon dealiasing algorithm is demonstrated through the processing of both synthetic and field seismic data

subgroups of lie type groups containing a unipotent radical abstract in this paper we show that if g is a lie type group and r a proper subgroup of g containing some unipotent radical then r has a nilpotent normal subgroup generated by long root subgroups and r is contained in a proper parabolic subgroup of g we also obtain some consequences of this result

1 twinnings of buildings in this paper we characterize twinnings of buildings by 1 twinnings and one further condition concerning twin apartments specialized to the spherical case we obtain new characterizations of the opposition relation in such buildings we also give a new description of the standard twin building of type widetilde a n 1

a curtis tits phan theorem for the twin building of type a n 1 abstract the curtis tits phan theory as laid out originally by bennett and shpectorov describes a way to employ tits lemma to obtain presentations of groups related to buildings as the universal completion of an amalgam of low rank groups it is formulated in terms of twin buildings but all concrete results so far were concerned with spherical buildings only we describe an explicit flip flop geometry for the twin building of type a n 1 associated to k t t 1 on which a unitary group su n k t t 1 related to a certain non degenerate hermitian form acts flag transitively and obtain a presentation for this group in terms of a rank 2 amalgam consisting of unitary groups this is the most natural generalization of the original result by phan for the unitary groups

on kreĭn s formula abstract kre n s formula provides a parametrization of the generalized resolvents and straus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a hilbert space in terms of nevanlinna families in a parameter space the aim of this note is to give a simple complete analytical proof of kre n s formula

existence and uniqueness of contractive solutions of some riccati equations abstract in this paper we establish criteria for the existence and uniqueness of contractive solutions k of the riccati equation kbk ka dk c 0 under the assumption that the spectra of a and d are disjoint

groups of lie type generated by long root elements in f4 k abstract let k be a field and g a quasi simple subgroup of the chevalley group f4 k we assume that g is generated by a class of abstract root subgroups such that there are a c with a c and any a is contained in a long root subgroup of f4 k we determine the possibilities for g and describe the embedding of g in f4 k

generalized resolvents and the boundary value problems for hermitian operators with gaps a hermitian operator a with gaps j j 1 j m is studied the self adjoint extensions which put exactly kj eigenvalues into each gap j j in particular for kj 0 1 j m the extensions preserving the gaps are described in terms of boundary conditions the generalized resolvents of the extensions with the indicated properties are described also a solvability criterion and description of all the solutions of the hamburger moment problem with supports in r j 1m j j are obtained in terms of the nevanlinna matrix

odd dimensional orthogonal groups as amalgams of unitary groups part 2 machine computations in the first part c bennett r gramlich c hoffman s shpectorov odd dimensional orthogonal groups as amalgams of unitary groups part 1 general simple connectedness j algebra 312 2007 426 444 a characterization of central quotients of the group spin 2n 1 q is given for n 3 and all odd prime powers q with the exception of the cases n 3 q 3 5 7 9 the present article treats these cases computationally thus completing the phan type theorem for the group spin 2n 1 q

boundary relations and their weyl families the concepts of boundary relations and the corresponding weyl families are introduced let s be a closed symmetric linear operator or more generally a closed symmetric relation in a hilbert space h let h be an auxiliary hilbert space let graphics and let jh be defined analogously a unitary relation g from the krein space h 2 j h to the kre in space h 2 j h is called a boundary relation for the adjoint s if ker gamma s the corresponding weyl family m lambda is de ned as the family of images of the defect subspaces n over cap lambda lambda is an element of c r under gamma here gamma need not be surjective and is even allowed to be multi valued while this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex hilbert space h and the class of unitary relations gamma h 2 j h h 2 j h it also generalizes the notion of so called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems moreover these new notions yield for instance the following realization theorem every h valued maximal dissipative for lambda is an element of c holomorphic family of linear relations is the weyl family of a boundary relation which is unique up to unitary equivalence if certain minimality conditions are satisfied further connections between analytic and spectral theoretical properties of weyl families and geometric properties of boundary relations are investigated and some applications are given

weak phan systems of type c n abstract the present article provides a classification of noncollapsing phan amalgams of type c n and of shape s s 2 over finite fields of square order distinct from four together with the results of r gramlich c hoffman s shpectorov j algebra 264 2003 358 384 this completes the proof of a phan type theorem for the group sp 2 n q for sufficiently large n and q

even dimensional orthogonal groups as amalgams of unitary groups abstract this article is part of the program described in c d bennett r gramlich c hoffman s shpectorov curtis phan tits theory in a a ivanov et al eds groups combinatorics and geometry proceedings of the durham conference on groups and geometries 2001 world scientific singapore 2003 pp 13 29 we provide presentations of even dimensional orthogonal groups a characterization of even dimensional orthogonal groups by certain amalgams of subgroups isomorphic to su 2 q 2 su 3 q 2 and su 2 q 2 su 2 q 2 over any finite field and a classification of related amalgams the results are obtained by diagram geometry geometric covering theory and analysis of amalgams

parabolic radon transform sampling and efficiency a good choice of the sampling in the transform domain is essential for a successful application of the parabolic radon transform the parabolic radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform fourier transform this leads to new and useful insights in the parabolic radon transform using nonuniform fourier theory we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general irregular sampling a significantly smaller sampling interval requires stabilization if diagonal stabilization is used no gain in resolution is obtained in contrast to conventional implementations the curvature sampling interval is proposed to be inversely proportional to the temporal frequency this results in improved quality of the transform and yields significant savings in computation time

the curtis tits presentation abstract let b be an irreducible spherical moufang building of rank 2 a an apartment of b and the set of roots of a with corresponding root subgroups a r aut b r let g ar r be the group of lie type b if is a fundamental system of denote by xr ar a r r and xrs xr xs for r s then the following let be the amalgamated product of the xrs amalgamated over the xr and g g the natural homomorphism then ker z g is known as the curtis tits presentation for g in this paper the proof of a generalization of this theorem which uses only local information is given

pitfalls of using conventional and discrete radon transforms on poorly sampled data the least square discrete radon transform drt is currently one of the most popular methods used in the suppression of multiples and other coherent noise events on irregularly sampled data gathers used for prestack true amplitude analysis unfortunately in the absence of a priori information this technique suffers from the same aliasing problems as fourier and conventional p methods although the drt is able to reconstruct the original image more accurately than conventional p transforms a harmful by product is an increase in the amplitude of aliased events in the transform domain in particular the drt will boost the amplitude of the aliases of true events that fall outside the p analysis window to help reconstruct the input data these amplified aliases degrade signal periodicity in the p domain if muted they can destroy subtle amplitude changes necessary for amplitude variation with offset avo analysis at the very least one should carefully evaluate the choice of analysis wind