maths.free › Functional Analysis

Functional Analysis

Banach and Hilbert spaces, operators, spectral theory.

ማስተማሪያ

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.

ተጨማሪ ትምህርት

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)

ከእነዚህ ትምህርት ቤቶች ውስጥ አንዳንዶቹ ከከፈቱ ጽሑፎች የተወሰዱ ናቸው፡ Wikipedia. Each lesson page names its source and licence.

ፊደላት

ለሙሉ መግለጫ፣ ምስል፣ እና በውስጡ ያለውን ፊደል ትርጓሜ ለማየት ማንኛውንም ምልክት ይጫኑ።

ጥያቄዎች

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.

የራስህ ችግር አለህ?
በፍታ ገጽ ላይ ጻፍ ወይም ጫን፦ እርምጃ ሁሉ፣ ምስል፣ መልሱ እስከምትጠይቅ ድረስ የተደበቀ ነው። መተላለፊያ →

ሌሎች

＋ Arithmetic 𝑥 Algebra △ Geometry ∿ Trigonometry ƒ Precalculus σ Statistics & Probability ⊢ Discrete Math & Logic ∫ Calculus ⊞ Linear Algebra ℕ Number Theory ẏ Differential Equations ∇ Multivariable Calculus ε Real Analysis ⋔ Combinatorics & Graph Theory ∈ Set Theory & Logic 𝔾 Abstract Algebra 𝑃 Probability Theory ≈ Numerical Methods ℂ Complex Analysis ◎ Topology μ Measure Theory κ Differential Geometry π₁ Algebraic Topology → Category Theory ∂ Partial Differential Equations ≋ Fluid Dynamics ∞ Frontiers