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Functional Analysis

Banach and Hilbert spaces, operators, spectral theory.

පාඩම්

Advanced Normed and Banach spaces Vector spaces with a length; completeness; the classical sequence and function spaces. sqrt(3^2 + 4^2) Advanced Hilbert spaces and the spectral theorem Inner products, orthonormal bases, Fourier series, and eigenvalues of operators. eigenvalues of [[2,1],[1,2]]

Linear algebra in infinitely many dimensions, where functions are the vectors. Quantum mechanics, PDEs and signal processing all live here; the spectral theorem is the eigenvalue story told for operators.

තවත් පාඩම්

Spaces of functions

Functional analysis Normed vector space Banach space Hilbert space Inner product space Complete metric space Sequence space Orthonormal basis Separable space

Operators

Bounded operator Linear map Dual space Compact operator Adjoint Self-adjoint operator Unitary operator Operator norm

The big theorems

Hahn–Banach theorem Open mapping theorem (functional analysis)Closed graph theorem Uniform boundedness principle Spectral theorem Riesz representation theorem Weak topology Banach fixed-point theorem

Fourier and applications

Fourier series Fourier transform Convolution Sobolev space Distribution (mathematics)

මෙම පාඩම් සමහර විවෘත පෙළ සිට අනුගත කර ඇත: Wikipedia. සෑම පාඩමකම පිටුව එහි මූලාශ්‍රය සහ බලපත්‍රය නම් කරයි.

මෙහිදී භාවිත කරන සංකේත

සම්පූර්ණ අර්ථ දැක්වීම සඳහා ඕනෑම සංකේතයක් ටැප්, පින්තූරයක්, සහ එය සෑම අකුරු අදහස් කරන්නේ කුමක්ද.

ජනතාව අහනවා ප්රශ්න

What is a Hilbert space?

A vector space with an inner product (so lengths and angles make sense) that is complete (no missing limit points). Square-integrable functions form one; quantum states live in one.

ඔයාට ඔයාගේම ප්‍රශ්නයක් තියෙනවද?
එය ටයිප් හෝ විසඳුම පිටුව මත එය ඇඳීමට: සෑම පියවරක්, පින්තූරයක්, ඔබ ඉල්ලා තෙක් පිළිතුර සැඟවුණු. විසඳන්න →

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