Strong Cesáro summability of triple Fourier integrals

• Autorzy: Mishra V. N. , Khatri K. , Mishra L. N.
• Języki publikacji: EN

Abstrakty

EN

The theory of summability is a very extensive field, which has various applications. We prove the following theorem. Assume ƒ ϵ L^∞(R3) with bounded support. If ƒ is continuous at some point (x₁, x₂, X₃) ϵ R³, then the triple Fourier integral of ƒ is strongly q-Casáro summable at (x₁, x₂, X₃) to the function value ƒ (x₁, x₂, X₃) for every 0 < q < ∞. Furthermore, if ƒ is continuous on some open subset G of R³, then the strong q-Cesáro summability of the triple Fourier integral of ƒ is locally uniform on G.

Słowa kluczowe

EN

triple Fourier transform and integral; inversion for-mula; partial (or Dirichlet) integral; (C, 1) summability and strong q - Cesaro summability

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 53
• Strony: 95--112
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Mishra V. N.

• Department of Applied Mathematics and Humanities Sardar Vallabhbhai National Institute of Technology Ichchhanath Mahadev Dumas Road Surat-395 007 (Gujarat), India

autor

Khatri K.

• Department of Applied Mathematics and Humanities Sardar Vallabhbhai National Institute of Technology Ichchhanath Mahadev Dumas Road Surat-395 007 (Gujarat), India

autor

Mishra L. N.

• Department of Mathematics National Institute of Technology Silchar - 788 010, District - Cachar (Assam), India
• L. 1627 Awadh Puri Colony Beniganj Phase - III, Opposite - Industrial Training Institute (I.T.I.) Ayodhya Main Road Faizabad - 224 001 (Uttar Pradesh), India

Bibliografia

• [1] Auscher P., Carro M.J., On relations between operators on RN, TN, and ZN, Studia Maths., 101(9192), 166-182.
• [2] Brown G., Feng D., Moricz F., Strong Cesáro summability of double Fourier integral, Acta Math. Hungar., 115(1-2)(2007), 1-12.
• [3] Hardy G.H., Divergent Series, Oxford University Press, London, 1949.
• [4] Khan H.H., On degree of approximation to a functions belonging to the class Lip(a,p), Indian Journal of Pure and Applied Mathematics, 5(1974), 132-136.
• [5] Moricz F., Strong Cesáro summability and statistical limit of Fourier integrals, Analysis, 25(2005), 79-86.
• [6] Mishra V.N., Khatri K., Mishra L.N., Product summability transform of conjugate series of Fourier series, International Journal of Mathematics and Mathematical Sciences Article, ID 298923 (2012), 13 pages, DOI: 10.1155/2012/298923.
• [7] Mishra V.N., Khatri K., Mishra L.N., Product (N,pn)(C, 1) summability of a sequence of Fourier coefficients, Mathematical Sciences (Springer open access), 6(38)(2012), DOI: 10.1186/2251 7456-6-38.
• [8] Mishra V.N., Khatri K., Mishra L.N., Using Linear Operators to Ap-proximate Signals of Lip(a,p), p > 1 -Class, Filomat, 27(2)(2013), 355-365.
• [9] Mishra V.N., Khatri K., Mishra L.N., Approximation of functions be-longing to class by summability of conjugate series of Fourier series, accepted Journal of Inequalities and Applications- a Springer Open Access Journal, 2012, 2012:296. DOI: 10.1186/1029-242X-2012-296.
• [10] Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, New Jersey, 1971.
• [11] Zygmund a., Trigonometric Series, Cambridge University Press, UK, 1959.