On Generalized Uncertainty Principle

We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation to analyze the quantum theory of gravity or string theory from the perspective of a complex function. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function δ̃(∆x,∆k, ǫ). We arrived at the string uncertainty principle from the analyticity condition of a newly introduced complex function which depends upon the UV cut-off. This non trivially modifies the quantum measurements, black hole physics and short distance geometries. Present analysis is based on the postulate that the Planck scale is the minimal length scale in nature and is in good agreement with the existance of maximum length scale in the nature. Both of these rely only on the analysis of the complex function and do not directly make use of any theory or the specific structure of the Hamiltonian. The Regge behaviour of the string spectrum with the quantization of area is also a natural consequence of our new complex function which may contain all the corrections operating in nature and reveal important clues to find the origins of the