共查询到20条相似文献,搜索用时 15 毫秒
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Min Chung 《Journal of Mathematical Analysis and Applications》2003,285(2):456-462
A Riesz basis is the image of an orthonormal basis under an invertible continuous linear mapping. In many interesting applications, perturbing an orthonormal basis in a controlled manner yields a Riesz basis. In this paper we find Riesz basis for of the form {bIk(x)sinλkx}, with bIk(x) bell functions, by perturbing the local sine and cosine orthonormal bases of Coifman and Meyer. 相似文献
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Edward Odell 《Journal of Functional Analysis》2010,258(2):604-615
We show that a construction of Johnson, Maurey and Schechtman leads to the existence of a weakly null sequence (fi) in ?2(∑Lpi), where pi↓1, so that for all ε>0 and 1<q?2, every subsequence of (fi) admits a block basis (1+ε)-equivalent to the Haar basis for Lq. We give an example of a reflexive Banach space having the unconditional subsequence property but not uniformly so. 相似文献
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L. Leindler 《Analysis Mathematica》2013,39(3):235-246
We prove two theorems including blocks of coefficients in the conditions. The aim of proving theorems of this type is to weaken the monotonicity assumptions of the coefficients. 相似文献
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Karel Stroethoff 《International Journal of Mathematical Education in Science & Technology》2013,44(5):793-794
In this note we give an elementary derivation for the power series expansions for the sine and the cosine function. 相似文献
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We consider complex-valued functions f ∈ L 1 (R+2),where R +:= [0,∞),and prove sufficient conditions under which the double sine Fourier transform f ss and the double cosine Fourier transform f cc belong to one of the two-dimensional Lipschitz classes Lip(α,β) for some 0 α,β≤ 1;or to one of the Zygmund classes Zyg(α,β) for some 0 α,β≤ 2.These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1 (R+2). 相似文献
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Mariya Georgievna Volkova Elena Ivanovna Olefir 《Journal of Mathematical Sciences》2014,200(3):389-398
A criterion of unconditional basis property for the families of vector-functions \( {E}_k(t):={c}_k{e}^{i{\uplambda}_k t},{c}_k\in {\mathbb{C}}^n,{\uplambda}_k\in \Lambda \) in the Cartesian product of n spaces L 2(0, a) without the restrictive condition inf k Im λ k > ?∞ is proved. 相似文献
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Several improvements are made to an algorithm of Higham and Smith for computing the matrix cosine. The original algorithm
scales the matrix by a power of 2 to bring the ∞-norm to 1 or less, evaluates the [8/8] Padé approximant, then uses the double-angle
formula cos (2A)=2cos 2A−I to recover the cosine of the original matrix. The first improvement is to phrase truncation error bounds in terms of ‖A2‖1/2 instead of the (no smaller and potentially much larger quantity) ‖A‖. The second is to choose the degree of the Padé approximant to minimize the computational cost subject to achieving a desired
truncation error. A third improvement is to use an absolute, rather than relative, error criterion in the choice of Padé approximant;
this allows the use of higher degree approximants without worsening an a priori error bound. Our theory and experiments show
that each of these modifications brings a reduction in computational cost. Moreover, because the modifications tend to reduce
the number of double-angle steps they usually result in a more accurate computed cosine in floating point arithmetic. We also
derive an algorithm for computing both cos (A) and sin (A), by adapting the ideas developed for the cosine and intertwining the cosine and sine double angle recurrences.
AMS subject classification 65F30
Numerical Analysis Report 461, Manchester Centre for Computational Mathematics, February 2005.
Gareth I. Hargreaves: This work was supported by an Engineering and Physical Sciences Research Council Ph.D. Studentship.
Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/T08739 and by a
Royal Society–Wolfson Research Merit Award. 相似文献
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We give an elementary calculus proof of the asymptotic formulas for the zeros of the q-sine and cosine functions which have been recently found numerically by Gosper and Suslov. Monotone convergent sequences of the lower and upper bounds for these zeros are constructed as an extension of our method. Improved asymptotics are found by a different method using the Lagrange inversion formula. Asymptotic formulas for the points of inflection of the basic sine and cosine functions are conjectured. Analytic continuation of the q-zeta function is discussed as an application. An interpretation of the zeros is given. 相似文献
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George A. Anastassiou 《Semigroup Forum》2008,76(1):149-158
Various L
p
form Opial type inequalities are given for cosine and sine operator functions with applications. 相似文献
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A comparative study of the functional equationsf(x+y)f(x–y)=f
2(x)–f
2(y),f(y){f(x+y)+f(x–y)}=f(x)f(2y) andf(x+y)+f(x–y)=2f(x){1–2f
2(y/2)} which characterise the sine function has been carried out. The zeros of the functionf satisfying any one of the above equations play a vital role in the investigations. The relation of the equationf(x+y)+f(x–y)=2f(x){1–2f
2(y/2)} with D'Alembert's equation,f(x+y)+f(x–y)=2f(x)f(y) and the sine-cosine equationg(x–y)=g(x)g(y) +f(x)f(y) has also been investigated. 相似文献
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A criterion for the unconditional basis property of eigenvectors for finite-rank perturbations of Volterra operators is given.
Considerations are based on functional models for non-self-adjoint operators and on the technique of the Muckenhoupt matrix
weights. 相似文献