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As Rigorous As It Gets
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As Rigorous As It Gets
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Math
About Me
Pritam Kayal 8/18/25 Pritam Kayal 8/18/25

On The Lp Boundedness of Reisz Projections and Its Implications on The Fourier Series

Proof of Convergence of the Partial Sums of the Fourier Series in Lp for 1<p<∞

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Pritam Kayal 8/8/25 Pritam Kayal 8/8/25

On the Convergence of Fejér Means in Lp

Generalization and Application of Theorem 8.14 (Folland)

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Pritam Kayal 6/25/25 Pritam Kayal 6/25/25

On Optimal Policies for Finite Horizon Markov Decision Problems

Extra theorems for chapter 4 of Martin L. Puterman’s “Markov Decision Processes“

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Pritam Kayal 4/30/25 Pritam Kayal 4/30/25

On the Convolution of Distributions with Compactly Supported Smooth Functions

Alternate Proof of Theorem 6.30 (Rudin’s Functional Analysis) Without Vector-Valued Integration

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Pritam Kayal 4/9/25 Pritam Kayal 4/9/25

Fundamental Solution of the Laplacian In All Dimensions

Finding the fundamental solution to the Laplacian in lower and higher dimensions

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Pritam Kayal 3/28/25 Pritam Kayal 3/28/25

The Fourier Transform of the Principal Value Distribution And Some Others

Solution to exercise 19 of chapter 9 of Folland’s text book

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Pritam Kayal 3/17/25 Pritam Kayal 3/17/25

Proving that a Function is the Fourier Transform of an L1 Function

Proving that a special function g is the Fourier Transform of an L1 function

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Pritam Kayal 3/16/25 Pritam Kayal 3/16/25

Non-Surjectivity of the Fourier Transform

A Proof that the Fourier transform from L1 to C0 is not Surjective

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Pritam Kayal 3/5/25 Pritam Kayal 3/5/25

Moore–Aronszajn Theorem

An Interesting Application of Metric Space Completion to ML

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Pritam Kayal 3/4/25 Pritam Kayal 3/4/25

Completion of Metric Spaces

Extention to Baby Rudin’s Chapter on Metric Spaces

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Pritam Kayal 2/18/25 Pritam Kayal 2/18/25

Jensen’s Inequality

Proof of Jensen’s Inequality for General Probability Spaces

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Pritam Kayal 2/3/25 Pritam Kayal 2/3/25

A Generalized Schur’s Test

Generalization of Folland’s Theorem 6.18

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Pritam Kayal 11/16/24 Pritam Kayal 11/16/24

Hessians And The Order of Partial Derivatives

When Can You Flip the Order of Partial Derivatives?

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Pritam Kayal 11/3/24 Pritam Kayal 11/3/24

On The Local Convexity of Lp Spaces for 0<p<1

Theorems on the relationship between the dimensionality of Lp spaces and underlying measures

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Pritam Kayal 9/24/24 Pritam Kayal 9/24/24

Lemma for Fubini’s Theorem

Lemma for Proving Folland’s Theorem 2.36

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Pritam Kayal 9/17/24 Pritam Kayal 9/17/24

Simple Proof of Intermediate Value Theorem

Simpler Proof of Baby Rudin’s Theorem 4.23

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