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Czasopisma help
  1. 8 Commentationes Mathematicae
  2. 5 Demonstratio Mathematica
  3. 3 Fasciculi Mathematici
  4. 3 Przegląd Elektrotechniczny
  5. 2 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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  1. 1 2023
  2. 1 2022
  3. 1 2020
  4. 3 2019
  5. 4 2017
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  1. 5 Szal B.
  2. 4 Rzepka A.
  3. 2 Halawa K.
  4. 2 Krantz R.
  5. 2 Kranz R.
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1
Content available A note on the MRBSVS class and its application to the uniform convergence and boundedness of sine series
100%
Szal B.
|
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tom 49
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nr 1
EN
A new class of \(\gamma\) rest bounded second variation sequences is defined. Some relationships between classes of considered sequences are proved. The results of Leindler [3] and author [8] are extended to our new class.
2
Content available On the rate of summability of Fourier series by means of the method of the Voronoi-Nörlund
100%
Stoiński S. l.
|
|
tom 49
|
nr 1
EN
In this note we present the theorem on the rate of pointwise summability of Fourier series by means of generalized Voronoi-Nörlund sums.
3
Content available remote On the rate of pointwise strong summability of Fourier series
100%
Łenski W. , Roszak B.
|
2004
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tom Vol. 37, nr 3
601--610
EN
There is introduced a modified local modulus of continuity as a measure of pointwise strong summability. The approximation versions of known results FuTraing Wang [6] and A. A. Zakharov [8] are obtained.
4
Content available A note on the uniform convergence and boundedness of a generalized class of sine series
100%
Szal B.
Commentationes Mathematicae
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2008
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tom 48
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nr 1
EN
In this paper we essentially extend the Leindler’s results concerning the uniform convergence and boundedness of a certain class of sine series.
5
Content available remote On pointwise approximation of functions by some matrix means of conjugate Fourier series
100%
Łenski W. , Szal B.
Fasciculi Mathematici
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2015
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tom Nr 55
91--108
EN
The results corresponding to some theorems of S. Lal [Tamkang J. Math., 31(4)(2000), 279-288] and the results of the authors [Banach Center Publ. 92(2011), 237-247] are shown. The same degrees of pointwise approximation as in mentioned papers by significantly weaker assumptions on considered functions are obtained. From presented pointwise results the estimation on norm approximation with essentialy better degrees are derived. Some special cases as corollaries for iteration of the Norlund or the Riesz method with the Euler one are also formulated.
6
Content available remote On the $L_1$-convergence of Fourier series
100%
Fridli S.
Studia Mathematica
|
1997
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tom 125
|
nr 2
161-174
EN
Since the trigonometric Fourier series of an integrable function does not necessarily converge to the function in the mean, several additional conditions have been devised to guarantee the convergence. For instance, sufficient conditions can be constructed by using the Fourier coefficients or the integral modulus of the corresponding function. In this paper we give a Hardy-Karamata type Tauberian condition on the Fourier coefficients and prove that it implies the convergence of the Fourier series in integral norm, almost everywhere, and if the function itself is in the real Hardy space, then also in the Hardy norm. We also compare it to the previously known conditions.
7
Content available remote On a generalized summation of Fourier series by means of the method of the Borel type
100%
Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2002
|
tom [Z] 42(2)
251-259
EN
In this note we present theorems on the pointwise summability of Fourier series by means of a generalized sums of the Borel type.
8
Content available remote On least squares estimation of Fourier coefficients and of the regression function
100%
Popiński W.
Applicationes Mathematicae
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1993-1995
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tom 22
|
nr 1
91-102
EN
The problem of nonparametric function fitting with the observation model $y_i = f(x_i) + η_i$, i=1,...,n, is considered, where $η_i$ are independent random variables with zero mean value and finite variance, and $x_i \in [a,b] \subset \R^1$, i=1,...,n, form a random sample from a distribution with density $ϱ \in L^1[a,b]$ and are independent of the errors $η_i$, i=1,...,n. The asymptotic properties of the estimator $\widehat{f}_{N(n)}(x) = \sum_{k=1}^{N(n)} \widehat{c}_ke_k(x)$ for $f \in L^2[a,b]$ and $\widehat{c}^{N(n)}=( \widehat{c}_1,..., \widehat{c}_{N(n)})^T$ obtained by the least squares method as well as the limits in probability of the estimators $\widehat{c}_k$, k=1,...,N, for fixed N, are studied in the case when the functions $e_k$, k=1,2,..., forming a complete orthonormal system in $L^2\[a,b\]$ are analytic.
9
Content available On the approximation of conjugate functions from \(L^{p}\) by some special matrix means of conjugate Fourier series
100%
Krantz R. , Rzepka A.
|
|
nr 2
EN
The results corresponding to some theorems of W. Łenski and B. Szal are shown. From the presented pointwise results the estimates on norm approximation are derived. Some special cases as corollaries are also formulated.
10
Content available remote Solving dual integral equations on Lebesgue spaces
100%
Ciaurri Ó. , Guadalupe J. J. , Pérez M. , Varona J. L.
Studia Mathematica
|
2000
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tom 142
|
nr 3
253-267
EN
We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh's type. We reformulate these equations giving a better description in terms of continuous operators on $L^p$ spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series $∑_{n=0}^{∞} c_n J_{μ+2n+1}$ which converges in the $L^p$-norm and almost everywhere, where $J_ν$ denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution.
11
Content available Study of current space phasor trajectory of the three-phase asynchronous motor with one phase open circuit fault
100%
Záskalický P.
Maszyny Elektryczne : zeszyty problemowe
|
2016
|
tom Nr 3 (111)
147--151
EN
The presented paper deals with the calculation of space phasor trajectory of the magnetization current of induction machine supplied by a converter under open-phase fault. To explore possibilities to reduce the impact of failure on the function of the machine is a winding node connected to zero point. Under open phase fault it is another possibility to improve behavior of the two-phase operation. There is still to apply a circular rotating magnetic field to the machine by imposing a 60o phase shift between the stator currents of the two supplied stator windings.
12
Content available remote A note on the MRBSV S class and its application to the uniform convergence and boundedness of sine series
100%
Szal B.
|
|
tom Vol. 49, [Z] 1
67-79
EN
A new class of γ rest bounded second variation sequences is dened. Some relationships between classes of considered sequences are proved. The results of Leindler [3] and author [8] are extended to our new class.
13
Content available remote On the rate of summability of Fourier series by means of the method of the Voronoi-Nörlund
100%
Stoiński S.
|
|
tom Vol. 49, [Z] 1
27-31
EN
In this note we present the theorem on the rate of pointwise summability of Fourier series by means of generalized Voronoi-Nörlund sums.
14
Content available remote A novel recursive method to reconstruct multivariate functions on the unit cube
100%
Zhang Z.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1568-1577
EN
Due to discontinuity on the boundary, traditional Fourier approximation does not work efficiently for d−variate functions on [0, 1]d. In this paper, we will give a recursive method to reconstruct/approximate functions on [0, 1]d well. The main process is as follows: We reconstruct a d−variate function by using all of its (d−1)–variate boundary functions and few d–variate Fourier coefficients. We reconstruct each (d−1)–variate boundary function given in the preceding reconstruction by using all of its (d−2)–variate boundary functions and few (d−1)–variate Fourier coefficients. Continuing this procedure, we finally reconstruct each univariate boundary function in the preceding reconstruction by using values of the function at two ends and few univariate Fourier coefficients. Our recursive method can reconstruct multivariate functions on the unit cube with much smaller error than traditional Fourier methods.
15
Content available remote Fourier series of functions involving higher-order ordered Bell polynomials
100%
Kim T. , Kim D. S. , Jang G.-W. , Jang L. C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1606-1617
EN
In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
16
Content available remote On the approximation of conjugate functions from Lp by some special matrix means of conjugate Fourier series
100%
Krantz R. , Rzepka A.
Commentationes Mathematicae
|
2014
|
tom Vol 54, No. 2
191--202
EN
The results corresponding to some theorems of W. Łenski and B. Szal are shown. From the presented pointwise results the estimates on norm approximation are derived. Some special cases as corollaries are also formulated.
17
Content available remote A note on the uniform convergence and boundedness of a generalized class of sine series
100%
Szal B.
Commentationes Mathematicae
|
2008
|
tom Vol. 48, [Z] 1
85-94
EN
In this paper we essentially extend the Leindler’s results concerning the uniform convergence and boundedness of a certain class of sine series.
18
Content available remote Some inequalities for coefficients of multiple Fourier series
100%
Musielak A.
|
2000
|
tom Vol. 33, nr 2
333-341
EN
The aim of this paper is to obtain some inequalities for Fourier coefficients in case of multiple trigonometric series, generalizing A. Zygmund's theorem on absolute convergence of Fourier series of functions of bounded variation satisfying Lipschitz condition with positive exponent.
19
Content available remote Geodesics in the Heisenberg Group
100%
Hajłasz P. , Zimmerman S.
|
2015
|
tom 3
|
nr 1
EN
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.
20
Content available SPAD timing jitter modeling using Fourier series
100%
Eyvazi K. , Karami M. A.
Optica Applicata
|
2023
|
tom Vol. 53, nr 2
239--248
EN
In this paper, a simple analytical model for the Gaussian’s peak response part of the timing jitter of single photon avalanche diodes (SPADs) is proposed using Fourier series in the multiplication time calculation. The multiplication time characterizes avalanche multiplication process speed in which low multiplication time suggests a swifter response time and a higher avalanche speed. This paper presents an analytical solution which results in a more accurate multiplication time. The model is verified for SPADs implemented in 0.15 and 0.18 μm standard CMOS process, and the accuracy of the proposed analytical method in full-width at half-maximum (FWHM) calculation is improved by 25% and 5% with respect to the numerical model, respectively.
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