Weighted inequalities for real-analytic functions in ℝ<Superscript>2</Superscript>

Let ƒ and g be real-analytic functions near the origin in ℝ². Given 1 < p < ∞, we obtain a characterization of the set of positive numbers ∈ and δ that ensures

Dubrovin Valuation Skew Group Rings

Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given. Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised. Received June 8, 1999, Revised June 4, 2001, Accepted July 20, 2001     

Computing determinantal representation of generalized inverses

We investigate implementation of the determinantal representation of generalized inverses for complex and rational matrices in the symbolic package MATHEMATICA. We also introduce an implementation which is applicable to sparse matrices.     

On convergence of wavelet packet expansions

It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.     

New Wavelet Bases and Isometric Between Symbolic Operators Spaces $$ {\text{OP}}S^{m}_{{1,\delta }} $$ and Kernel Distributions Spaces

In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distribution spaces     

Factorization Index for Completely Positive Graphs

In this paper, we prove that the set of all factorization indices of a completely positive graph has no gaps. In other words, we give an affirmative answer to a question raised by N. Kogan and A. Berman [8] in the case of completely positive graphs. Received December 9, 1997, Accepted May 16, 2002     

Similarity-Invariant Subspaces and Similarity-Preserving Linear Maps

In this paper, the similarity-invariant subspaces of B(H), which is the Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given. Received November 3, 1999, Revised September 20, 2000, Accepted February 5, 2001     

Transcendence of Certain Trigonometric Series

In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The proof of the theorem is based on a criterion for linear independence over a number field. Received November 9, 1999, Accepted February 5, 2001     

Gerbes and Duality

We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes; these objects are mathematical constructions generalizing U(1) bundles and are similarly classified by quantized charges. We address the duality maps in terms of the potentials rather than on their field strengths and show the quantum equivalence between dual theories which in turn allows a rigorous proof of a generalized Dirac quantization condition on the couplings. Our approach needs the introduction of an auxiliary form satisfying a global constraint which in the case of 1-form potentials coincides with the quantization of the magnetic flux. We apply our global approach to refine the proof of the duality equivalence between the d=11 supermembrane and d=10 IIA Dirichlet supermembrane.