共查询到20条相似文献,搜索用时 0 毫秒
1.
Jan Stochel 《Proceedings of the American Mathematical Society》1998,126(2):431-440
It is shown that an -tuple of bounded linear operators on a complex Hilbert space, which is positive definite in the sense of Halmos, must be commutative. Some generalizations of this result to the case of pairs of unbounded operators are obtained.
2.
We prove q-Taylor series for Jackson q-difference operators. Absolute and uniform convergence to the original function are proved for analytic functions. We derive interpolation results for entire functions of q-exponential growth which is less than lnq−1, 0<q<1, from its values at the nodes , a is a non-zero complex number with absolute and uniform convergence criteria. 相似文献
3.
Very recently Aral and Gupta [1] introduced q analogue of Baskakov-Durrmeyer operators. In the present paper we extend the studies, we establish the recurrence relations for the central moments and obtain an asymptotic formula. Also in the end we propose modified q-Baskakov-Durrmeyer operators, from which one can obtain better approximation results over compact interval. 相似文献
4.
Yilmaz Simsek 《Journal of Mathematical Analysis and Applications》2006,318(1):333-351
The main purpose of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q-L-function. In particular, by using these generating functions, we will construct new generating functions which produce q-Dedekind type sums and q-Dedekind type sums attached to Dirichlet character. We also give the relations between these sums and Dedekind sums. Furthermore, by using *-product which is given in this paper, we will give the relation between Dedekind sums and q-L function as well. 相似文献
5.
Vijay Gupta 《Journal of Mathematical Analysis and Applications》2011,377(2):471-480
In the present paper we propose the q analogue of the modified Beta operators. We apply q-derivatives to obtain the central moments of the discrete q-Beta operators. A direct result in terms of modulus of continuity for the q operators is also established. We have also used the properties of q integral to establish the recurrence formula for the moments of q analogue of the modified Beta operators. We also establish an asymptotic formula. In the end we have also present the modification of such q operators so as to have better estimate. 相似文献
6.
Fethi Bouzeffour 《Journal of Mathematical Analysis and Applications》2007,336(2):833-848
We study fractional transforms associated with q-Bessel operator which is useful to inverse q-Riemann-Liouville and q-Weyl transforms. 相似文献
7.
Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah–Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah–Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities. 相似文献
8.
Qiu-Ming Luo 《Journal of Mathematical Analysis and Applications》2010,363(1):7-18
We show some results for the q-Bernoulli and q-Euler polynomials. The formulas in series of the Carlitz's q-Stirling numbers of the second kind are also considered. The q-analogues of well-known formulas are derived from these results. 相似文献
9.
In this paper, the approximation properties of q-Durrmeyer operators Dn,q(f;x) for f∈C[0,1] are discussed. The exact class of continuous functions satisfying approximation process limn→∞Dn,q(f;x)=f(x) is determined. The results of the paper provide an elaboration of the previously-known ones on operators Dn,q. 相似文献
10.
Hao Pan 《Discrete Mathematics》2006,306(17):2118-2127
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers. 相似文献
11.
Jian-Ping Fang 《Journal of Mathematical Analysis and Applications》2008,339(2):845-852
In this paper, we apply q-exponential operator to get some general q-Chu-Vandermonde's identities. 相似文献
12.
Jian-Ping Fang 《Journal of Mathematical Analysis and Applications》2007,332(2):1393-1407
In this paper, we construct a new q-exponential operator and obtain some operator identities. Using these operator identities, we give a formal extension of Jackson's transformation formula. A formal extension of Bailey's summation and an extension of the Sears terminating balanced transformation formula are also derived by our operator method. In addition, we also derive several interesting a formal extensions involving multiple sum about three terms of Sears transformation formula and Heine's transformation formula. 相似文献
13.
In this paper, we use the q-Chu–Vandermonde formula to prove two new operator identities, which are the extensions of Liu's results. These two q-exponential operator identities are used to derive some q-summation formulas and q-integrals. 相似文献
14.
Victor J.W. Guo Martin Rubey Jiang Zeng 《Journal of Combinatorial Theory, Series A》2006,113(7):1501-1515
Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salié's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations. 相似文献
15.
Burak ?ekero?lu Fatma Ta?delen 《Journal of Mathematical Analysis and Applications》2007,326(2):896-907
Almost four decades ago, Konhauser introduced and studied a pair of biorthogonal polynomials
16.
17.
A special case of the big q-Jacobi polynomials Pn(x;a,b,c;q), which corresponds to a=b=−c, is shown to satisfy a discrete orthogonality relation for imaginary values of the parameter a (outside of its commonly known domain 0<a<q−1). Since Pn(x;qα,qα,−qα;q) tend to Gegenbauer (or ultraspherical) polynomials in the limit as q→1, this family represents another q-extension of these classical polynomials, different from the continuous q-ultraspherical polynomials of Rogers. For a dual family with respect to the polynomials Pn(x;a,a,−a;q) (i.e., for dual discrete q-ultraspherical polynomials) we also find new orthogonality relations with extremal measures. 相似文献
18.
We derive discrete orthogonality relations for polynomials, dual to little and big q-Jacobi polynomials. This derivation essentially requires use of bases, consisting of eigenvectors of certain self-adjoint operators, which are representable by a Jacobi matrix. Recurrence relations for these polynomials are also given. 相似文献
19.
Taekyun Kim 《Journal of Mathematical Analysis and Applications》2002,273(1):236-242
The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570). 相似文献
20.
In this work we present a derivation for the complete asymptotic expansions of Euler?s q-exponential function and Jackson?s q-gamma function via Mellin transform. These formulas are valid everywhere, uniformly on any compact subset of the complex plane. 相似文献