Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) * Give appropriate graphs and required codes. * Make use of inequalities if you think that required. *You are supposed to use kreszig for reference. (E) (Em)" Σ Holder inequality: Σls & j=1 where p > 1 and 1 1 + P Cauchy-Schwarz inequality: P j=1 Minkowski inequality: + j=1 1. m=1 + k=1 where p > 1. Σ m=1 Problem 26: Interpolation Theorems Problem Statement: Interpolation theorems allow for the estimation of operators between different function spaces. Tasks: a) Riesz-Thorin Interpolation Theorem: State the Riesz-Thorin Interpolation Theorem. b) Application to Linear Operators: Use the Riesz-Thorin Theorem to determine the boundedness of a linear operator T between LP spaces for intermediate values of p. c) Marcinkiewicz Interpolation Theorem: State the Marcinkiewicz Interpolation Theorem and compare it with the Riesz-Thorin Theorem. d) Visualization: Provide an example where interpolation is used to estimate operator norms between different LP spaces. Include graphs illustrating the operator's action across various p.