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Approximation of signals of class \(Lip(\alpha , p)\) by linear operators. (English) Zbl 1213.42006
The authors extend several theorems pertaining to error estimates of trigonometric-Fourier approximation. They use in their theorems very general classes of lower triangular regular summability matrix methods having non-negative entries, assuming only certain almost monotonicity and regularity assumptions.

MSC:
42A10 Trigonometric approximation
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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[1] Chandra, P., A note on degree of approximation by norlund and Riesz operators, Mat. vestnik, 42, 9-10, (1990) · Zbl 0725.42004
[2] Chandra, P., Trigonometric approximation of functions in Lp-norm, J. math. anal. appl., 275, 13-26, (2002) · Zbl 1011.42001
[3] Gil, M.I., Estimates for entries of matrix valued functions of infinite matrices, Math. phys. anal. geom, 11, 175-186, (2008) · Zbl 1194.47019
[4] Leindler, L., Trigonometric approximation in Lp-norm, J. math. anal. appl., 302, 129-136, (2005) · Zbl 1057.42004
[5] Mittal, M.L.; Rhoades, B.E., Approximations by matrix means of double Fourier series to continuous functions in two variables functions, Radovi mat., 9, 77-99, (1999) · Zbl 0953.42007
[6] Mittal, M.L.; Rhoades, B.E., On the degree of approximation of continuous functions by using linear operators on their Fourier series, Int. J. math., game theor., algebra, 9, 259-267, (1999) · Zbl 0958.42001
[7] Mittal, M.L.; Rhoades, B.E., Degree of approximation to functions in a normed space, J. comput. anal. appl., 2, 1-10, (2000) · Zbl 0945.42001
[8] Mittal, M.L.; Rhoades, B.E., Degree of approximation of functions in the holder metric, Radovi mat., 10, 61-75, (2001) · Zbl 0995.41010
[9] Mittal, M.L.; Singh, U.; Mishra, V.N.; Priti, S.; Mittal, S.S., Approximation of functions belonging to lip(ξ(t),p)-class by means of conjugate Fourier series using linear operators, Ind. J. math., 47, 217-229, (2005) · Zbl 1103.42001
[10] Mittal, M.L.; Rhoades, B.E.; Mishra, V.N., Approximation of signals (functions) belonging to the weighted W(lp, ξ(t)), (p⩾1)-class by linear operators, Int. J. math. math. sci. ID 53538, 1-10, (2006) · Zbl 1126.42001
[11] Mittal, M.L.; Rhoades, B.E.; Mishra, V.N.; Singh, Uaday, Using infinite matrices to approximate functions of class lip(α,p) using trigonometric polynomials, J. math. anal. appl., 326, 667-676, (2007) · Zbl 1106.42001
[12] Proakis, J.G., Digital communications, (1995), McGraw-Hill New York
[13] Psarakis, E.Z.; Moustakides, G.V., An L2-based method for the design of 1-D zero phase FIR digital filters, IEEE trans. circuits syst. I. fundamental theor. appl., 44, 591-601, (1997) · Zbl 0891.93057
[14] Mohpatra, R.N.; Russell, D.C., Some direct and inverse theorems in approximation of functions, J. austral. math. soc. ser. A, 34, 143-154, (1983) · Zbl 0518.42013
[15] Quade, E.S., Trigonometric approximation in the Mean, Duke math. J., 3, 529-542, (1937) · Zbl 0017.20501
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