NBHM 2024 Solutions | NBHM 2024 Mathematics Question 28 Solution | Functional Analysis NBHM Question | Operator Norm Solution NBHM 2024 | Normed Space and Linear Operator Explanation |NBHM 2024 Math Functional Analysis Problem

In this video, we solve a challenging NBHM 2024 Mathematics problem on functional analysis involving the operator norm. The problem is from Question 28, where we analyze a normed space (Xa,∥⋅∥a)(Xa​,∥⋅∥a​) of continuous functions and determine the operator norm of a given linear operator SS.

Key Highlights:

Explanation of the norm ∥f∥a=sup⁡x≥0eax∣f(x)∣∥f∥a​=supx≥0​eax∣f(x)∣.
Detailed calculation of the operator norm of SS, defined by Sf(x)=∫0xe−b(x−y)f(y) dySf(x)=∫0x​e−b(x−y)f(y)dy.
Step-by-step derivation with intuitive explanations for better understanding.
Techniques that are essential for topics like linear operators, normed spaces, and integration in functional analysis.

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