Intrinsic Lagrangian regularity and principal symbols

Continue with general homogeneous maps, proper supports and complete symbol spaces, including the derivative-loss symbol classes and full asymptotic proofs.

These lessons develop the frequency-graph criterion, ordinary phase representations, Sobolev improvement, Maslov lines and the global principal-symbol exact sequence.

Follow the reading sequence · Earlier stationary-phase proofs and foundations

The mathematical components include their complete selected earlier proofs, editable sources and retained component licences. The tangent-model identification is developed in the next lesson; the full course remains unfinished.

Reading and source files

• intrinsic frequency graphs · editable source
• measure and l2 · editable source
• fourier l2 · editable source
• dyadic endpoint · editable source
• quadratic multiplier foundations · editable source
• metric localization · editable source
• gauss transform estimates · editable source
• ordinary operator calculus · editable source
• conic frequency coordinates · editable source
• coordinate and wavefront localization · editable source
• conic parametrices and localization · editable source
• prescribed phase representation · editable source
• sobolev order refinement · editable source
• relative maslov line · editable source
• global principal symbol · editable source

Exact component proof map · Source and validation record