Generalized growth of entire harmonic functions

• Autorzy: Srivastava G. S.
• Języki publikacji: EN

Abstrakty

EN

Let H(x), x = (x₁, x₂, ... , x_n), be an entire harmonic function in Rⁿ.Fryant and Shankar [1] had obtained growth properties of H explicitly in terms of its Fourier coeffcients. In this paper, we obtain the characterizations of generalized order and type and introduce the generalized lower order for H. Special case of functions of slow growth has also been considered. Our results generalize some of the results obtained in [1].

Słowa kluczowe

EN

harmonic function; spherical harmonics; entire function; Fourier coefficients; order; type; generalized order; generalized type; lower order

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2008
• Tom: Nr 40
• Strony: 79--89
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Srivastava G. S.

• Department of Mathematics, Indian Institute of Technology, Roorkee-247 667, Uttarkhand, India,

Bibliografia

• [1]FRYANT A. , SHANKAR H . , Fourier coefficients and growth of harmonic functions, Internat. J. Math. Math. Sci., 0(3)(1987), 443-452.
• [2]JUNE J A O. P., KAPOOR G. P., BAJPAI S. K., On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine. Angew. Math., 282(1976), 53-67.
• [3]JUNEJA O. P., KAPOOR G. P., BAJPAI S. K., On the (p,q)-type and lower (p,q)-type of an entire function, J. Reine. Angew. Math., 290(1977), 180-189.
• [4]KAPOOR G. P., NAUTIYAL A., Polynomial approximation of an entire function of slow growth, J. Approximation Theory, 32(1981), 64-75.
• [5]LEVIN B. JA, Distribution of zero of entire functions, G I T T L , Moscow, 1950, English translation, Trans. Math. Monographs, Vol.5, Amer. Math. Soc. Providence, R.I. 1964.
• [6]SEREMETA M.N., On the connection between the growth of the maximum modulus of an entire function and the modulii of the coefficients of its power series expansion, Trans. Amer. Math. Soc., 88(1970), 291-301.
• [7]SHAH S.M., Polynomial approximation of an entire function and generalized orders, J. Approximation Theory, 19(4)(1977), 315-324.
• [8]SRIVASTAVA G.S., A note on logarithmic proximate orders, Istanbul Univ.Fen. Fak. Mecm., Serie A, 35(1970), 79-83.
• [9]STEIN E.M., WEISS G., Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey 1971.