Harmonic Functions Starlike in the Unit Disk

Harmonic Functions in the Unit Disk

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Wiener’s Tauberian Theorem in L(g//k) and Harmonic Functions in the Unit Disk

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in L1(G//K) , the space of radial integrable functions on G = SU(1 , 1) , so that I = L1(G//K) or I = L0(G//K)—the ideal of L 1(G//K) functions whose integral is zero. This is then used to prove a generalization of Furstenberg’s theorem which characterizes harmonic functions on th...

WIENER'S TAUBERIAN THEOREM IN Ll{G//K) AND HARMONIC FUNCTIONS IN THE UNIT DISK

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal / in Ll(G//K), the space of radial integrable functions on G = SU{1, 1), so that / = Ll(G//K) or / = L^(G//K)—the ideal of Ll(G//K) functions whose integral is zero. This is then used to prove a generalization of Furstenberg's theorem which characterizes harmonic functions on the un...

On Meromorphic Harmonic Starlike Functions with Missing Coefficients

On Harmonic Uniformly Starlike Functions Defined by an Integral Operator

Using the integral operator, we define and study a generalized family of complex-valued harmonic functions that are univalent, sense-preserving and are associated with uniformly harmonic functions in the unit disk. We obtain coefficient inequalities, extreme points and distortion bounds for the functions in our class. The results obtained for the our class reduce to the corresponding results fo...