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The basic tool is the decomposition ofN pairs of free charged bosons with respect toglN and the commuting withglN Lie algebra of infinite matrices?l.
      
We prove as the main result thatM is weakly symmetric with respect toG1 and complex conjugation.
      
Let ${\mathcal B}_u$ be the orbit of $u\in{\mathcal X}_2$ with respect to this action.
      
For instance, we find that |f(u)| ≤ L(u) + O(ε2/3), where L(u) is the Boas-Kac-Lukosz 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.
      
It is shown that these transformations are bounded in the space $L^p,\ 1>amp;lt;p>amp;lt;\infty,$ with respect to the measure that makes LB selfadjoint.
      
[6] regarding boundedness of maximal functions with respect to rectangles of lacunary directions, and prove a result regarding the cardinality of subsets of arithmetic progressions in sets of the type described above.
      
Further we obtain a complete classification of refinement equations with positive coefficients (in the case of finitely many terms) with respect to the existence of continuous or integrable compactly supported solutions.
      
The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work.
      
Greedy algorithms and bestm-term approximation with respect to biorthogonal systems
      
The article extends upon previous work by Temlyakov, Konyagin, and Wojtaszczyk on comparing the error of certain greedy algorithms with that of best m-term approximation with respect to a general biorthogonal system in a Banach space X.
      
We prove that the exponential localization of a frame with respect to an orthonormal
      
Then μ is absolutely continuous with respect to Lebesgue measure on the sphere.
      
Wavelet Decomposition of Spherical Vector Fields with Respect to Sources
      
Furthermore, they are compared with respect to accuracy and efficiency with other methods to approximate canonical windows associated with Gabor frames.
      
We introduce a family of linear differential operators ${\cal K}^n =(-i)^nP_n^{\cal M}(i\frac{d}{dt})$, called the chromatic derivatives associated with M, which are orthonormal with respect to a suitably defined scalar product.
      
Suppose that the scaling functions are invariant with respect to some finite group action.
      
Using this approach, we prove that the matrix representation of a Fourier Integral Operator with respect to a Parseval frame of shearlets is sparse and well-organized.
      
In this paper, a mathematical model with respect to the optimal identification of the thermodynamic parameters is established.
      
The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ?--mixing random fields.
      
respectively, Ri∈C(R×[0, ∞)×[0, ∞), (0, ∞)) (i=1, 2) are ω-periodic with respect to their first arguments, respectively.
      
 

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