Distributions, kernels and analytic singularities

All 72 authored lessons and their used prerequisite routes are self-checked by the writing AI. The reader includes exact prerequisite copies, editable sources and a verified offline archive.

Start with the learning guide · Supplied prerequisite proofs · Offline reader and editable sources

  1. Distributions as kernels of continuous operators
  2. When a kernel is smooth
  3. Tensor products and parameter-dependent distributions
  4. Jets, supported distributions and local operators
  5. Locality forces continuity
  6. Compatible jets on closed sets
  7. Paths control supported distributions
  8. Order, positivity and distributional limits
  9. Local data and compatible products
  10. Weak equations and classical functions
  11. Boundary flux and weak identities
  12. Lipschitz graphs and surface measures
  13. Cauchy kernels and distributional boundary limits
  14. Gluing holomorphic sides
  15. Holomorphic boundaries in convex cones
  16. Finite parts of singular powers
  17. Complex powers at a boundary
  18. Homogeneous extensions and angular moments
  19. Euler equations and the order of singularities
  20. Point sources and complex Gaussian kernels
  21. Convolution as addition of supports
  22. Causal integration of complex order
  23. Positive derivatives and canonical representatives
  24. Compactness and complex-line positivity
  25. Zero hypersurfaces as curvature measures
  26. Odd powers and collapsing hyperbolas
  27. Causal point sources and characteristic cones
  28. Radial sources and quadratic logarithms
  29. Curved Cauchy kernels and complex pole cutoffs
  30. Convex supports and convolution cancellation
  31. Fundamental solutions, continuation and approximation
  32. Regularity across a distinguished variable
  33. Convolution estimates and weak-gradient embeddings
  34. Compact forcing, moments and positive error kernels
  35. Spherical convolution and support control
  36. Tensor order and integral kernel bounds
  37. Regular level sets and transverse convolution
  38. Real zeros and merging poles
  39. Wave powers and complex potentials
  40. Tempered growth and spectral cutoffs
  41. Separated frequencies and distributional order
  42. Spectral localization and constant equations
  43. Convolution equations and logarithmic tails
  44. Euler chains and Fourier eigenspaces
  45. Positive kernels and spectral measures
  46. Spectral gaps and explicit Fourier distributions
  47. Finite spectra, boundary poles and resolvent limits
  48. Tempered tensors and stationary Gaussian equations
  49. Reciprocal tails and zero-frequency jumps
  50. Rational spectra and origin matching
  51. Radial powers and the logarithmic endpoint
  52. Planar rotations and angular spectra
  53. Complex quadratic powers and the Cauchy kernel
  54. Radial decay and spherical Fourier spectra
  55. Boundary powers and angular Fourier spectra
  56. Bernoulli series and Poisson summation
  57. Periodic Green functions and boundary spectra
  58. Resolvent sampling and positive periodization
  59. Sharp bounds for compact spectra
  60. Cosine crossings and spectral-gap bounds
  61. Compact factors and homogeneous equations
  62. Fourier-Laplace slices and boundary poles
  63. Gaussian norms and entire uncertainty
  64. Quadratic transforms and tempered images
  65. Quadratic phases and curved spectra
  66. Dispersion, measure obstructions and tempered point sources
  67. Stationary concentration and point jets
  68. Polynomial phases and Fourier tails
  69. Hölder Gaussian bounds and operator remainders
  70. Classical finite-order preparation and division
  71. Smooth complex equations and flat remainders
  72. An oriented coordinate normal form for a real finite-order zero