Analytic elements in p-adic analysis

Content: 1. Absolute values and norms -- 2. Infraconnected sets -- 3. Monotonous and circular filters -- 4. Ultrametric absolute values and valuation functions v(h, u) on K(x) -- 5. Hensel Lemma -- 6. Ultrametric field extensions -- 7. Ultraproducts and spherically complete extensions -- 8. A study in [symbol], the p[symbol]-th roots of 1 -- 9. Algebras R(D) -- 10. The analytic elements -- 11. Composition of analytic elements -- 12. Mult(H(D), U[symbol]) -- 13. Power series -- 14. Factorization of analytic elements -- 15. The Mittag-Leffler theorem -- 16. Maximal ideals of codimension 1 -- 17. Dual of a space H(D) -- 18. Algebras H(D) -- 19. Derivative of analytic elements -- 20. Valuation functions for analytic elements -- 21. Elements vanishing along a filter -- 22. Quasi-minorated elements -- 23. Values and zeros of power series -- 24. Quasi-invertible elements -- 25. Zeros theorem for power series -- 26. Image of a disk -- 27. Strictly injective analytic elements -- 28. Logarithm and exponential -- 29. A finite increasing property -- 30. Maximum principle -- 31. Analytic elements meromorphic in a hole -- 32. Motzkin factorization -- 33. Applications of the Motzkin factorization -- 34. Maximum in a circle with holes -- 35. T-filters and T-sequences -- 36. Examples and counter-examples about T-filters -- 37. Characteristic property of the T-filters -- 38. Applications of T-filters -- 39. Integrally closed algebras H(D) -- 40. Absolute values on H(D) -- 41. Distinguished circular filters -- 42. Maximal ideals of infinite codimension -- 43. Idempotent T-sequences -- 44. T-polar sequences -- 45. Analytic extension through a T-filter -- 46. Algebra [symbol] -- 47. Meromorphic products -- 48. Collapsing meromorphic products -- 49. Injectivity, Mittag-Leffler series and Motzkin products -- 50. Analytic functions and analytic elements -- 51. Infinite van der Monde matrices -- 52. p-adic analytic interpolation -- 53. Analytic elements with a zero derivative -- 54. Generalities on the differential equation y' = fy in H(D) -- 55. The differential equation y' = fy in algebras H(D) -- 56. The equation y' = fy in zero residue characteristic -- 57. The equation y' = fy in [symbol] with f not quasi-invertible -- 58. The equation y' = fy in [symbol] with f quasi-invertible -- 59. Residues and equation y' = fy -- 60. Equation g' = fg with [symbol] H(D) -- 61. The p-adic Fourier transform.