The hottest Functional Analysis Substack posts right now

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Linear Algebra Is Not Enough!

Quantum Formalism • 59 implied HN points • 01 Jun 20
🔬 Science Mathematics Quantum Mechanics Functional Analysis Topology Group Theory
  1. Linear Algebra is foundational in quantum mechanics but may not be enough if dealing with infinite-dimensional Hilbert spaces.
  2. To fully understand quantum mechanics, one needs to delve into Functional Analysis along with other mathematical branches like Topology, Measure Theory, and Group Theory.
  3. The newsletter focuses on explaining the mathematical formalism of quantum mechanics through easily understandable posts on relevant topics.

Influential Mathematicians: Maurice René Fréchet

Quantum Formalism • 19 implied HN points • 23 Jul 20
🔬 Science Mathematics Quantum Mechanics Statistics Topology Functional Analysis
  1. Maurice René Fréchet, a disciple of Jacques Hadamard, made significant contributions to mathematics through his work on metric spaces and abstract spaces, laying the groundwork for modern mathematical formalism, including quantum mechanics.
  2. Fréchet's research on functional analysis has influenced the development of the quantum formalism, allowing for the creation of abstract concepts crucial in understanding quantum mechanics.
  3. The Riesz–Fréchet representation theorem plays a key role in making mathematical sense of Dirac's bra-ket notation used in quantum mechanics, showcasing the impact of Fréchet's work in this field.

Influential Mathematicians: Jacques Hadamard

Quantum Formalism • 19 implied HN points • 17 Jun 20
🔬 Science Mathematics Quantum Mechanics Functional Analysis Books
  1. Jacques Hadamard's early struggles in mathematics did not deter him from becoming an influential mathematician of the 20th century.
  2. Hadamard's work on functions of a complex variable and entire functions laid significant groundwork for future mathematical developments.
  3. Although Hadamard did not directly contribute to quantum formalism, his work on functional analysis played a crucial role in its mathematical foundation.

Influential Mathematicians: Frigyes Riesz

Quantum Formalism • 0 implied HN points • 15 Jul 20
🔬 Science Mathematics Quantum Mechanics Functional Analysis Physics Theory
  1. Frigyes Riesz was a significant mathematician who made key contributions to functional analysis and operator theory, impacting areas like physics and Hilbert spaces.
  2. His work, including the Riesz-Fischer theorem, influenced the development of quantum theory, showing the unitary equivalence of different quantum theories.
  3. Riesz is known for foundational work in Functional Analysis, which is crucial for the mathematical formalism of quantum mechanics, and concepts like Dirac's bracket notation make sense thanks to Riesz representation theorem.
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