scholarly journals Matrix transformations and Walsh's equiconvergence theorem

2005 ◽  
Vol 2005 (16) ◽  
pp. 2647-2653 ◽  
Author(s):  
Chikkanna R. Selvaraj ◽  
Suguna Selvaraj
Keyword(s):  
Matrix Transformation ◽  
Matrix Transformations ◽  
Large Disk ◽  
Complex Sequences ◽  
Equiconvergence Theorem ◽  
The Difference

In 1977, Jacob definesGα, for any0≤α<∞, as the set of all complex sequencesxsuch that|xk|1/k≤α. In this paper, we applyGu−Gvmatrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that theGu−Gvmatrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.

Matrix transformations between some classes of sequences

1970 ◽  
Vol 68 (1) ◽  
pp. 99-104 ◽  
Author(s):  
C. G. Lascarides ◽  
I. J. Maddox
Keyword(s):  
Matrix Transformation ◽  
Matrix Transformations ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
The Matrix ◽  
Complex Sequences ◽  
Class Of Matrices

Let A = (ank) be an infinite matrix of complex numbers ank (n, k = 1, 2,…) and X, Y two subsets of the space s of complex sequences. We say that the matrix A defines a (matrix) transformation from X into Y, and we denote it by writing A: X → Y, if for every sequence x = (xk)∈X the sequence Ax = (An(x)) is in Y, where An(x) = Σankxk and the sum without limits is always taken from k = 1 to k = ∞. The sequence Ax is called the transformation of x by the matrix A. By (X, Y) we denote the class of matrices A such that A: X → Y.

scholarly journals Matrix Transformations and Disk of Convergence in Interpolation Processes

2008 ◽  
Vol 2008 ◽  
pp. 1-11
Author(s):  
Chikkanna R. Selvaraj ◽  
Suguna Selvaraj
Keyword(s):  
Lagrange Interpolation ◽  
Hermite Interpolation ◽  
Matrix Transformation ◽  
Matrix Transformations ◽  
Taylor Polynomial ◽  
Lagrange Polynomial ◽  
Birkhoff Interpolation ◽  
Partial Sum ◽  
The Difference ◽  
Definition Of

Let denote the set of functions analytic in but not on . Walsh proved that the difference of the Lagrange polynomial interpolant of and the partial sum of the Taylor polynomial of converges to zero on a larger set than the domain of definition of . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and Hermite-Birkhoff interpolation processes in a similar manner. In this paper, we apply a certain matrix transformation on the sequences of operators given in the above-mentioned interpolation processes to prove the convergence in larger disks.

scholarly journals Generalised regularity and compactness of matrix operators

2020 ◽  
Vol 12 (2) ◽  
pp. 57-66
Author(s):  
E. Malkowsky
Keyword(s):  
Measure Of Noncompactness ◽  
Linear Operators ◽  
Matrix Transformations ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Regular Matrix ◽  
Hausdorff Measure Of Noncompactness ◽  
Complex Sequences ◽  
Matrix Operators ◽  
Convergent Sequences

A well-known result by Cohen and Dunford ([2], 1937) characterises the class of all regular compact linear operators. It follows that a regular matrix transformation cannot be compact. This means that if c denotes the set of all complex sequences of complex numbers, then an infinite matrix that maps c into c and preserves the limits cannot be compact. We obtained this result in a different way applying the theory of BK spaces from functional analysis and summability, and using the Hausdorff measure of noncompactness. Furthermore, we present the extension of this result to matrix transformations between the spaces c and the spaces of strongly summable sequences by the Cesaro method of order 1, and of strongly convergent sequences. We present new unified proofs for our main results.

scholarly journals Matrix transformations and application to perturbed problems of some sequence spaces equations with operators

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5123-5130
Author(s):  
Malafosse de ◽  
Ali Fares ◽  
Ali Ayad
Keyword(s):  
Linear Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
Complex Sequences ◽  
Perturbed Equation

Given any sequence z = (zn)n?1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n?1 such that y/z = (yn/zn)n?1 ? E; in particular, cz = s(c) z denotes the set of all sequences y such that y/z converges. Starting with the equation Fx = Fb we deal with some perturbed equation of the form ? + Fx = Fb, where ? is a linear space of sequences. In this way we solve the previous equation where ? =(Ea)T and (E,F) ? {(l?,c), (c0,l?), (c0,c), (lp,c), (lp,l?), (w0,l?)} with p ? 1, and T is a triangle.

A Design of Observers of Control State and Uncertainty via Transformation of T-S Fuzzy Models

2018 ◽  
Vol 22 (2) ◽  
pp. 194-202 ◽  
Author(s):  
Hugang Han ◽  
Yuki Sueyama ◽  
Chun-Jun Chen ◽  
◽  
Keyword(s):  
Fuzzy Model ◽  
The State ◽  
Point Of View ◽  
Matrix Transformation ◽  
Control Performance ◽  
Fuzzy Models ◽  
State Observers ◽  
Traditional Sense ◽  
The Difference ◽  
Control State

When employing the widely used T-S fuzzy model as a model to represent a system concerned with controller designs, it is necessary to consider the precision of the model from the point of view of control performance. Adding a term called uncertainty in the T-S fuzzy model to compensate for the difference between the concerned system and its T-S fuzzy model, this paper focuses on a design of observers for both the control state and uncertainty. Unlike a state observer in the traditional sense, which is usually designed as a whole, the state is divided into two parts by performing a unique matrix transformation; and two observers from the two divided parts of the state are designed separately in order to eliminate the influence of the uncertainty. Finally, an observer of the aforementioned uncertainty based on one of the state observers is suggested.

A SET OF NEW PARANORMED DIFFERENCE SEQUENCE SPACES AND THEIR MATRIX TRANSFORMATIONS

2013 ◽  
Vol 06 (03) ◽  
pp. 1350040 ◽  
Author(s):  
P. Baliarsingh
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Structures ◽  
The Matrix ◽  
The Difference ◽  
Positive Integers ◽  
Difference Sequence Spaces

In this paper, by using a new difference operator Δj, the author likes to introduce new classes of paranormed difference sequence spaces X(Δj, u, v; p) for X ∈ {ℓ∞, c, c0} and investigates their topological structures, where (un) and (vn) are two sequences satisfying certain conditions. The difference operator Δjis defined by Δj(xj) = jxj- (j + 1)xj+1for all j ∈ ℕ, the set of positive integers. Also, we determine the α-, β- and γ-duals of these classes. Furthermore, the matrix transformations from these classes to the sequence spaces ℓ∞(q), c0(q) and c(q) have been characterized.

A possible quantitative Mueller matrix transformation technique for anisotropic scattering media/Eine mögliche quantitative Müller-Matrix-Transformations-Technik für anisotrope streuende Medien

2013 ◽  
Vol 2 (2) ◽  
Author(s):  
Honghui He ◽  
Nan Zeng ◽  
E Du ◽  
Yihong Guo ◽  
Dongzhi Li ◽  
...  
Keyword(s):  
Biological Tissues ◽  
Anisotropic Scattering ◽  
Mueller Matrix ◽  
Polar Coordinates ◽  
Matrix Transformation ◽  
Matrix Transformations ◽  
Matrix Elements ◽  
Scattering Media ◽  
Structural And Optical Properties ◽  
Analytical Functions

AbstractBy conducting both the experiments on samples containing well-aligned fibers and Monte Carlo simulations based on the sphere cylinder scattering model (SCSM), we present a Mueller matrix transformation (MMT) method for quantitatively characterizing the properties of anisotropic scattering media. We obtained a set of parameters by fitting the Mueller matrix elements to trigonometric curves in polar coordinates. These new parameters can be expressed as analytical functions of the Mueller matrix elements and display simple relationships to the structural and optical properties of the anisotropic scattering media, such as the anisotropy, the direction of the fibers, and the sizes of the scatterers. Experimental results on biological tissues show that these new parameters can be used in biomedical research. However, further studies are still necessary to correlate the MMT parameters to pathological features.

Laser TV Color Gamut Transform Based on FPGA

2013 ◽  
Vol 401-403 ◽  
pp. 1904-1907
Author(s):  
Chao Xue ◽  
Yi Zhong Yu
Keyword(s):  
Video Signal ◽  
Matrix Transformation ◽  
Matrix Transformations ◽  
Median Filtering ◽  
Color Gamut ◽  
Simulation Test ◽  
Conversion Model ◽  
Conversion Algorithm ◽  
Wide Color Gamut ◽  
Color Video

Aiming at the wide color gamut feature of the Laser TV, Color gamut transform using matrix transformations is proposed.And the conversion results are optimized by using median filtering.the theory of the median filtering and matrix transformation is introduced in this paper. Gamut conversion model of laser video signal is built based on FPGA.The function and realization of each model in the circuit is analyzed and the simulation test is conducted finally. The results verify that gamut conversion algorithm can convert the fluorescent domain video signal to the laser-domain video signal. The color video signal can reappear in the Laser TV clearly.

scholarly journals Calculations on Matrix Transformations Involving an Infinite Tridiagonal Matrix

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 218
Author(s):  
Ali Fares ◽  
Ali Ayad ◽  
Bruno de Malafosse
Keyword(s):  
Tridiagonal Matrix ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
Complex Sequences

Given any sequence z=znn≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y=ynn≥1 such that y/z=yn/znn≥1∈E; in particular, sz0 denotes the set of all sequences y such that y/z tends to zero. Here, we consider the infinite tridiagonal matrix Br,s,t˜, obtained from the triangle Br,s,t, by deleting its first row. Then we determine the sets of all positive sequences a=ann≥1 such that EaBr,s,t˜⊂Ea, where E=ℓ∞, c0, or c. These results extend some recent results.

Convergence field of Abel’s summation method

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Peter Letavaj
Keyword(s):  
Metric Space ◽  
Linear Subspace ◽  
Summation Method ◽  
Matrix Transformation ◽  
Matrix Transformations ◽  
Regular Matrix ◽  
Porous Set ◽  
Linear Metric Space ◽  
Bounded Sequences

AbstractLet F(A) denote the set of all bounded sequences summable by Abel’s method. It is known, that F(A) is a linear subspace of the linear metric space (S, ρ) of all bounded sequences endowed with the sup metric. It is shown in [KOSTYRKO, P.: Convergence fields of regular matrix transformations 2, Tatra Mt. Math. Publ. 40 (2008), 143–147] that the convergence field of a regular matrix transformation is a σ-porous set. We show that F(A) is very porous in S.

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