Concept

Riesz representation theorem

Related lectures (15)

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

Lax-Milgram: Variational Problems and Riesz's Theorem

Explores the Lax-Milgram theorem, variational problems, and Riesz's representation theorem in linear elliptic problems.

Herglotz Representation Theorem

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Hilbertian Bounded Operators

Introduces Hilbert operators, covering their properties, C*-algebras, and the Fourier transform's unitarity.

Kernel Methods: RKHS and Kernels

Explores RKHS, positive definite kernels, and the Moore-Aronszajn theorem in kernel methods.

Heisenberg Groups: Introduction

Introduces the Heisenberg groups, covering representation theory and unique properties.

Principles of Quantum Mechanics

Covers the principles of quantum mechanics, including the Measurement Principle and Max Born Rule.

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Asset Pricing: Risk-Neutral Measure and State Prices

Covers risk-neutral measure, state prices, utility functions, and risk aversion in asset pricing.

Discrete Symmetries Introduction

Introduces discrete symmetries, operators, and tetraquarks in quantum field theory.

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Wigner Theorem; Translation Symmetry

Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.

The Adjoint Representation

Introduces the concept of the adjoint representation in Lie algebras.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.