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Fourier–Bros–Iagolnitzer transform: Holmgren's uniqueness theorem, Overview & Definitions

In mathematics, the FBI transform or Fourier–Bros–Iagolnitzer transform is a generalization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer in order to characterise the local analyticity of functions (or distributions) on Rn. The transform provides an alternative approach to analytic wave front…

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Fourier–Bros–Iagolnitzer transform topic overview

The analysis highlights Holmgren's uniqueness theorem, Overview and Definitions as prominent areas in the source structure around Fourier–Bros–Iagolnitzer transform.

Related topics
21
Source areas
6
Connected nodes
27
Extracted relationships
1
Related term clusters
20
Bridge connections
27

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 12 topics
Holmgren's uniqueness theorem · 5 topics
Criterion for local analyticity · 1 topics
Definitions · 1 topics
Inversion formula · 1 topics
The analytic wave front set · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definitions

Inversion formula

Criterion for local analyticity

Holmgren's uniqueness theorem

The analytic wave front set

For the semantics nerds

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Advanced semantic analysis

How Fourier–Bros–Iagolnitzer transform connects Entity context

The extracted context around Fourier–Bros–Iagolnitzer transform shows recurring relationship patterns in the source. For example, Fourier–Bros–Iagolnitzer transform → generalization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer in order to characterise the local analyticity of fun…. Use these groups to spot repeated connection types before inspecting the individual relationships.

Fourier–Bros–Iagolnitzer transform

Top relations

is a · 1
Fourier–Bros–Iagolnitzer transform → generalization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer in order to characterise the local analyticity of fun…

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

analytic transform theorem analyticity fbi local iagolnitzer wave front distributions mathematics isbn fourier bros rn elliptic differential uniqueness mathematical sato

Fourier–Bros–Iagolnitzer transform relationships Subject–Predicate–Object triples

TTTA extracted 1 structured relationship around Fourier–Bros–Iagolnitzer transform. Examples in this analysis include Fourier–Bros–Iagolnitzer transform → is a → generalization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer in order to characterise the local analyticity of fun…. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Fourier–Bros–Iagolnitzer transformis ageneralization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer in order to characterise the local analyticity of fun…0.90text

Related concept clusters Related term clusters

The concept neighborhoods around Fourier–Bros–Iagolnitzer transform bring nearby vocabulary together. In this analysis, examples include Rn, Fbi and Distribution. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Fourier–Bros–Iagolnitzer transform
    • Rn
    • Fbi
    • Distribution
    • Distributions
    • Formula
    • Function
    • Inversion
    • Transform
    • Analyticity
    • Local
    • Developed
    • Defined
  • fourier–bros–iagolnitzer transform
    • Iagolnitzer
    • Distribution
    • Rn
    • Analyticity
    • Fbi
    • Formula
    • Function
    • Inversion
    • Local
    • Distributions
    • Front
    • Transform
  • fourier transform
    • Rn
    • Formula
    • Function
    • Inversion
    • Distributions
    • Front
    • Transform
    • Wave
    • Analyticity
    • Local
    • Defined
    • Distribution
  • local analyticity
    • Mathematical
    • Bros
    • Analyticity
    • Iagolnitzer
    • Local
    • Fbi
    • Defined
    • Princeton
    • Set
    • Transform
    • Uniqueness
    • Fourier
  • wave front sets
    • Front
    • Wave
    • Set
    • Defined
    • Holmgren's
    • Transform
    • Analytic
    • Analyticity
    • Fbi
    • Theorem
    • Developed
    • Cauchy
  • fourier inversion formula
    • Function
    • Inversion
    • Rn
    • Transform
    • Distributions
    • Formula
    • Fourier
    • Analyticity
    • Local
    • Defined
    • Developed
    • Distribution
  • real analytic function
    • Inversion
    • Transform
    • Theorem
    • Differential
    • Elliptic
    • Front
    • Wave
    • Cauchy
    • Classical
    • Coefficients
    • Defined
    • Equations
  • criterion for local analyticity
    • Mathematical
    • Bros
    • Analyticity
    • Iagolnitzer
    • Local
    • Fbi
    • Defined
    • Princeton
    • Set
    • Transform
    • Uniqueness
    • Fourier

Connections between topic areas Semantic bridges

For Fourier–Bros–Iagolnitzer transform, one of the stronger structural bridges in this analysis connects Fourier–Bros–Iagolnitzer transform with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Fourier–Bros–Iagolnitzer transform — Overview · splits 15 ⟂ 13
Fourier–Bros–Iagolnitzer transform — Holmgren's uniqueness theorem · splits 22 ⟂ 6

Map overview Semantic statistics

Fourier–Bros–Iagolnitzer transform

Nodes28
Edges27
Triples1
Avg. degree1.93
Density0.071429
Components1

Source & methodology

TTTA analyzes the structure around Fourier–Bros–Iagolnitzer transform to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Holmgren's uniqueness theorem, Overview & Definitions, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Fourier–Bros–Iagolnitzer transform · EN edition · Analysis: TopicsToTalkAbout

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