maths.free › Functional Analysis

Functional Analysis

Banach and Hilbert spaces, operators, spectral theory.

ପାଠ୍ୟ

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.

ଅଧିକ ପାଠ୍ୟ

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)

ଏହି ଶିକ୍ଷାଗୁଡ଼ିକ ମଧ୍ୟରୁ କିଛି ଖୋଲା ପାଠ୍ୟରୁ ଆୟୋଜିତ ହୋଇଛି: Wikipedia. ପ୍ରତ୍ୟେକ ଶିକ୍ଷାଦାନ ପୃଷ୍ଠା ଏହାର ଉତ୍ସ ଏବଂ ଲାଇସେନ୍ସ ନାମ ଦେଇଥାଏ ।

ଏଠାରେ ବ୍ୟବହୃତ ପ୍ରତୀକଗୁଡିକ

ସମ୍ପୂର୍ଣ୍ଣ ବର୍ଣ୍ଣନା ପାଇଁ ଯେକୌଣସି ପ୍ରତୀକକୁ ଟ୍ୟାପ କରନ୍ତୁ, ଗୋଟିଏ ଚିତ୍ର, ଏବଂ ଏଥିରେ ଥିବା ପ୍ରତ୍ୟେକ ଅକ୍ଷରର ଅର୍ଥ କଣ।

ଲୋକମାନେ ପଚାରୁଥିବା ପ୍ରଶ୍ନ

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.

ଆପଣଙ୍କର ନିଜ ସମସ୍ୟା ଅଛି କି?
ଏହାକୁ ଟାଇପ କରନ୍ତୁ କିମ୍ବା ସମାଧାନକାରୀ ପୃଷ୍ଠାରେ ଅଙ୍କନ କରନ୍ତୁ: ପ୍ରତ୍ୟେକ ପଦକ୍ଷେପ, ଗୋଟିଏ ଚିତ୍ର, ଉତ୍ତର ଲୁକ୍କାୟିତ ଯେପର୍ଯ୍ୟନ୍ତ ଆପଣ ପଚାରନ୍ତି। ସମାଧାନ କରନ୍ତୁ →

ଅନ୍ୟାନ୍ୟ ବୃକ୍ଷ

＋ 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