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Abstract IN THIS THESIS ,WE GENERALIZE MANY RESULTS IN SOME PREVIOUS PAPERS [4,26,29,41,48,50,] TO THE CASE OF VECTOR VALUED FUNCTIONS ON GROUPS TO BANACH SPACES AND WE SUCCEED TO OBTAIN THE NECESSARY AND SUFFICIENT CONDITIONS FOR STRONG CONVERGENCE OF FOURIER SERIES OF BOCHNER INTEGRABLE VECTOR VALUED FUNCTIONS DEFINED ON A CIRCLE GROUP TO BANACH SPACES. ALSO,WE INTRODUCE AND STUDY THE NOTION OF VECTOR VALUED FOURIER SERIES ON SOLENOID GROUPS TO A COMPLEX BANACH SPACE. |