On Burgess's theorem and related problems

Let be a graph. We determine all graphs which are -like. We also prove that if are graphs, then in order that each -like continuum be -indecomposable for some it is necessary and sufficient that if is a graph, then is not -like for some integer with . This generalizes a well known theorem of Burgess.

     

Statistical extensions of some classical Tauberian theorems

Hardy's well-known Tauberian theorem for Cesàro means says that if the sequence satisfies and , then . In this paper it is shown that the hypothesis can be replaced by the weaker assumption of the statistical limit: st-lim , i.e., for every , . Similarly, the ``one-sided' Tauberian theorem of Landau and Schmidt's Tauberian theorem for the Abel method are extended by replacing and with st-lim and st-lim , respectively. The Hardy-Littlewood Tauberian theorem for Borel summability is also extended by replacing , where is a continuous parameter, with , and further replacing it by -st-lim , where is the Borel matrix method.

     

Normalizers of the congruence subgroups of the Hecke group II

Let . Let be an ideal of and let be the maximal ideal of such that . Then . In particular, if is square free, then is self-normalized in .

     

Annihilating a subspace of with the sign of a continuous function

Let be a -finite, nonatomic, Baire measure space. Let be a finite dimensional subspace of . There is a bounded, continuous function, , defined on , such that

(1) for all , and (2) almost everywhere.

     

Finite generation properties for fuchsian group von Neumann algebras tensor

We prove that the algebra , a free group with finitely many generators, contains a subnormal operator such that the linear span of the set is weakly dense in . This is the analogue for the factor , finite, of a well known fact about the unilateral shift on a Hilbert space : the linear span of all the monomials is weakly dense in .

We also show that for a suitable space of square summable analytic functions, if is the projection from the Hilbert space of all square summable functions onto and is the unbounded operator of multiplication by on , then the (unbounded) operator is nonzero (with nonzero domain).

     

On a theorem of Barbara Schmid

Let be a finite group and a complex representation. Barbara Schmid has shown that the algebra of invariant polynomial functions on the vector space is generated by homogeneous polynomials of degree at most , where is the largest degree of a generator in a minimal generating set for , and is the complex regular representation of . In this note we give a new proof of this result, and at the same time extend it to fields whose characteristic is larger than , the order of the group .

     

Injective resolutions of Noetherian rings and cogenerators

We give new construction of injective resolutions of complexes and bimodules. Applying this construction to an injective resolution of a Noetherian ring, we construct a -embedding cogenerator for the category of modules of projective dimension . Moreover, for a Noetherian projective -algebra , we show that satisfies the Auslander condition if and only if the flat dimension of every -module is equal to or larger than the one of the injective hull .

     

Tilting up iterated tilted algebras

We show that, if is a representation-finite iterated tilted algebra of euclidean type , then there exist a sequence of algebras , and a sequence of modules , where , such that each is an APR-tilting -module, or an APR-cotilting -module, and is tilted representation-finite.

     

Collapsibility of and some related CW complexes

Let denote the order complex of the partition lattice. The natural -action on the set induces an -action on . We show that the regular CW complex is collapsible. Even more, we show that is collapsible, where is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual way several previous results regarding the multiplicity of the trivial character in the -representation on .

     

Adjacency preserving mappings of invariant subspaces of a null system

In the space of invariant -dimensional subspaces of a null system in -dimensional projective space, W.L. Chow characterized the basic group of transformations as all the bijections , for which both and preserve adjacency. In the present paper we show that the two conditions is a surjection and preserves adjacency are sufficient to characterize the basic group. At the end of this paper we give an application to Lie geometry.

     

Carleson measures and some classes of meromorphic functions

For let be the Möbius transformation defined by , and let be the Green's function of the unit disk . We construct an analytic function belonging to for all , , but not belonging to meromorphic in and for any , . This gives a clear difference as compared to the analytic case where the corresponding function spaces ( and ) are same.

     

Extensions of holomorphic maps through hypersurfaces and relations to the Hartogs extensions in infinite dimension

A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map from into , where is a hypersurface in a complex Banach manifold and is a hyperbolic Banach space. Under various assumptions on , and we show that can be extended to a holomorphic map from into . Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property.

     

Periodic hyperfunctions and Fourier series

Every periodic hyperfunction is a bounded hyperfunction and can be represented as an infinite sum of derivatives of bounded continuous periodic functions. Also, Fourier coefficients of periodic hyperfunctions are of infra-exponential growth in , i.e., for every and every . This is a natural generalization of the polynomial growth of the Fourier coefficients of distributions.

To show these we introduce the space of hyperfunctions of growth which generalizes the space of distributions of growth and represent generalized functions as the initial values of smooth solutions of the heat equation.

     

On Euler products associated with noncuspidal metaplectic forms

In this paper, we obtain an Euler product with functional equation associated to a noncuspidal metaplectic form on the double cover of . Zagier's idea of Rankin-Selberg method is used to define the convolution of and the -function.

     

A criterion for splitting -algebras in tensor products

The goal of the paper is to prove the following theorem: if , are unital -algebras, simple and nuclear, then any -subalgebra of the -tensor product of and , which contains the tensor product of with the scalar multiples of the unit of , splits in the -tensor product of with some -subalgebra of .

     

Involutions with

Let be a smooth involution on a closed -dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each component of the fixed point set of vanish in positive dimension. In this paper, we estimate the least possible lower bound of dim if does not bound.

     

An uncertainty principle for convolution operators on discrete groups

Consider a discrete group and a bounded self-adjoint convolution operator on ; let be the spectrum of . The spectral theorem gives a unitary isomorphism between and a direct sum , where , and is a regular Borel measure supported on . Through this isomorphism corresponds to multiplication by the identity function on each summand. We prove that a nonzero function and its transform cannot be simultaneously concentrated on sets , such that and the cardinality of are both small. This can be regarded as an extension to this context of Heisenberg's classical uncertainty principle.

     

Multiple symmetric positive solutions for a second order boundary value problem

For the second order boundary value problem, , , , where growth conditions are imposed on which yield the existence of at least three symmetric positive solutions.

     

Maximal estimates for the -dimensional Walsh-Fourier series

The -dimensional dyadic martingale Hardy spaces are introduced and it is proved that the maximal operator of the means of a Walsh-Fourier series is bounded from to and is of weak type , provided that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain that the means of a function converge a.e. to the function in question. Moreover, we prove that the means are uniformly bounded on whenever . Thus, in case , the means converge to in norm. The same results are proved for the conjugate means, too.

     

A bound on the reduction number of a primary ideal

Let be a local ring of positive dimension and let be an -primary ideal. We denote the reduction number of by , which is the smallest integer such that for some reduction of In this paper we give an upper bound on in terms of numerical invariants which are related with the Hilbert coefficients of when is Cohen-Macaulay. If , it is known that where denotes the multiplicity of If in Corollary 1.5 we prove where is the first Hilbert coefficient of From this bound several results follow. Theorem 1.3 gives an upper bound on in a more general setting.