On the method of approximation by families of linear polynomial operators.
On the Mixed Modulus of Smoothness and a Class of Double Fourier Series
MSC 2010: 42A32; 42A20In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above.
On the Multiresolution analysis of abstract Hilbert spaces
On the non-equivalence of rearranged Walsh and trigonometric systems in
We consider the question of whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in for some p ≠ 2. We show that this question is closely related to a combinatorial problem. This enables us to prove non-equivalence for a number of rearrangements. Previously this was known for the Walsh-Paley order only.
On the Nörlund means of Vilenkin-Fourier series
We prove and discuss some new -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of general Nörlund...
On the number of Daubechies scaling functions and a conjecture of Chyzak et al.
On the order of magnitude of Walsh-Fourier transform
For a Lebesgue integrable complex-valued function defined on let be its Walsh-Fourier transform. The Riemann-Lebesgue lemma says that as . But in general, there is no definite rate at which the Walsh-Fourier transform tends to zero. In fact, the Walsh-Fourier transform of an integrable function can tend to zero as slowly as we wish. Therefore, it is interesting to know for functions of which subclasses of there is a definite rate at which the Walsh-Fourier transform tends to zero. We...
On The Orthogonality Measure Of The ...-Pollaczek Polynomials.
On the -adic spectral analysis and multiwavelet on .
On the (P) summability of a sequence of Fourier coefficients
On the partial sums of Walsh-Fourier series
We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.
On the pointwise estimation of Cesàro kernel of negative order with respect to Walsh-Paley system.
On the pointwise multiplication in Besov and Lizorkin-Triebel spaces.
On the pointwise strong approximation by (C,1)(E,1) means
We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.
On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.
On the polynomials orthogonal in the interval with the weight function
On the Product of Functions in BMO and H
The point-wise product of a function of bounded mean oscillation with a function of the Hardy space is not locally integrable in general. However, in view of the duality between and , we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with holomorphic functions in the unit disc, the converse is also valid: every holomorphic...
On the product theory of singular integrals.
We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in...
On the proof of Erdős' inequality
Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality for a constrained polynomial of degree at most , initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval and establish a new asymptotically sharp inequality.
On the properties of oscillation and almost periodicity of certain convolutions