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Simple modules over the multiparameter quantum function algebra at roots of 1


We construct essentially all the irreducible modules for the multiparameter quantum function algebraF?φ[G], whereG is a simple simply connected complex algebraic group, and ? is a root of unity.


Virasoro Algebra, Dedekind ηfunction and Specialized Macdonald Identities


We study Nekrasov's deformed partition function $Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ of 5dimensional supersymmetric


This is done by reducing the problem to the case of bipartite quivers of a special form and using a function DP on three matrices, which is a mixture of the determinant and two pfaffians.


When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form.


For instance, we find that f(u) ≤ L(u) + O(ε2/3), where L(u) is the BoasKacLukosz bound, and show by means of an example that this version is the sharpest possible with respect to its behaviour as a function of ε as ε ↓ 0.


When a function does not belong to such a space, the sampling series may converge, not to the object function but to an "alias" of it, and an aliasing error is said to occur.


We also dealt with the question of how large the supremum KS of all numbers f(u) is with f the Fourier transform of a nonnegative integrable function F and f(0) = 1, f(ku) ≤ ε for k ∈ S.


To that end we generalize the method given in [1] to include Fourier transforms f of probability measures on R and a certain generalized function h, and we show that the numbers KS, MS are assumed as f(u), Mh for certain allowed f,h.


Poisson Summation, the Ambiguity Function, and the Theory of WeylHeisenberg Frames


Gabor timefrequency lattices are sets of functions of the form $g_{m \alpha , n \beta} (t) =e^{2 \pi i \alpha m t}g(tn \beta)$ generated from a given function $g(t)$ by discrete translations in time and frequency.


We investigate the $L_p$error of approximation to a function $f\in L_p({\Bbb T}^d)$ by a linear combination $\sum_{k}c_ke_k$ of $n$


These means are given by some function λ and generalize the wellknown BochnerRiesz means.


We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth.


In addition, if the scaling functions have at least asymptotic linear phase, then we prove that they converge to the "sinc" function and their corresponding orthonormal wavelets converge to the "difference" of two sinc functions.


The frame operator of this sequence is expressed as a matrixvalued function multiplying a vectorvalued function.


Associated to a given D is a setT (A, D), which is the attractor of an affine iterated function system, satisfyingT=∪d∈D(T+d).


A corollary is the existence of wavelet sets, and hence of singlefunction wavelets, for arbitrary expansive matrix dilations on L2(?n).


Let S ? ?n+1 be the graph of the function ? :[1, 1]n → ? defined by ? (x1, …, xn) = ∑j=1nxjαj, with1>amp;lt;α1 ≤ … ≤ αn, let σ the Euclidean area measure on S.




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