Alphabeta MathPersonal research
Control duality and nonlinear estimates
Develop the real Hilbert observation-to-control chain and endpoint feedback construction alongside polynomial, time-integrability and exterior algebra bounds needed for nonlinear endpoint and trajectory control.
1 · Prerequisites
- Simultaneous Sobolev extension and localization
- Real-order Hˢ as weighted Fourier distributions
- Young's convolution inequality under Countable Choice
- Holder's inequality for integrals, including the endpoint cases
- Fourier transform of a product with one integrable transform
- Fourier inversion on Schwartz space
- Schwartz functions are dense in the Fourier Bessel-potential norm
- The sharp trace theorem: boundedness and range in the fractional space
- Distributional derivatives are polynomial Fourier multipliers
- Plancherel theorem
- The Axiom of Choice
- Integer-order Sobolev spaces and their norms
- Integer-order Sobolev spaces are Banach
- Schwartz space and its seminorms
- The Lᵖ trace operator on a bounded C¹ domain
2 · Logical flowchart
Arrows show item dependencies. A grouped prerequisite node points to items that use one or more of its members; their exact links are listed above.
3 · Items
Lemma