Multidimensional Singular Integrals and Integral Equations

Contents......Page all_21026_to_00269.cpc0005.djvu
Preface......Page all_21026_to_00269.cpc0009.djvu
§1. Review of previous work......Page all_21026_to_00269.cpc0011.djvu
§2. Some theorems on linear equations in Banach spaces......Page all_21026_to_00269.cpc0031.djvu
§3. Stereographic projection......Page all_21026_to_00269.cpc0040.djvu
§4. Completely continuous operators......Page all_21026_to_00269.cpc0042.djvu
§5. Basic concepts......Page all_21026_to_00269.cpc0047.djvu
§6. Lipschitz conditions......Page all_21026_to_00269.cpc0056.djvu
§7. Order of singular integrals at infinity......Page all_21026_to_00269.cpc0060.djvu
§8. Differentiation of integrals with a weak singularity......Page all_21026_to_00269.cpc0069.djvu
§9. Compounding of singular and ordinary integrals......Page all_21026_to_00269.cpc0073.djvu
§10. Compounding of double singular integrals......Page all_21026_to_00269.cpc0077.djvu
§11. The concept of a singular operator......Page all_21026_to_00269.cpc0080.djvu
§12. Compounding of double singular integrals. The symbol......Page all_21026_to_00269.cpc0081.djvu
§13. Compounding of multidimensional singular integrals......Page all_21026_to_00269.cpc0082.djvu
§14. Formulae for reference......Page all_21026_to_00269.cpc0084.djvu
§15. Product of the operators A_1 and A_n......Page all_21026_to_00269.cpc0087.djvu
§16. Product of the operators A_2 and A_n......Page all_21026_to_00269.cpc0091.djvu
§17. Calculation of \kappa_{1,m}......Page all_21026_to_00269.cpc0093.djvu
§18. Symbol of a multidimensional singular integral......Page all_21026_to_00269.cpc0096.djvu
§19. Fourier transform of a singular kernel......Page all_21026_to_00269.cpc0103.djvu
§20. Fourier transform of a kernel and the symbol of a singular operator......Page all_21026_to_00269.cpc0107.djvu
§21. Transformation of the symbol under change of variables......Page all_21026_to_00269.cpc0114.djvu
§22. Differentiability of the symbol......Page all_21026_to_00269.cpc0119.djvu
§23. The conditions for the continuity of the symbol......Page all_21026_to_00269.cpc0122.djvu
§24. The simplest corollaries from the Fourier transform. First theorem on boundedness in L_2 space......Page all_21026_to_00269.cpc0126.djvu
§25. Symbol dependent on the pole. Second theorem on boundedness in L_2 space......Page all_21026_to_00269.cpc0129.djvu
§26. On the boundedness of a singular integral operator in L_p space......Page all_21026_to_00269.cpc0133.djvu
§27. Integrals taken over any manifold......Page all_21026_to_00269.cpc0140.djvu
§28. Differential properties of singular integrals......Page all_21026_to_00269.cpc0141.djvu
§29. More about the differentiation of integrals with a weak singularity......Page all_21026_to_00269.cpc0144.djvu
§30. Polyharmonic potentials......Page all_21026_to_00269.cpc0145.djvu
§31. Series of spherical functions......Page all_21026_to_00269.cpc0146.djvu
§32. Differential properties of the symbol and the characteristic......Page all_21026_to_00269.cpc0158.djvu
§33. Rule for the multiplication of the symbols in the general case......Page all_21026_to_00269.cpc0160.djvu
§34. Conjugate singular operator......Page all_21026_to_00269.cpc0164.djvu
§35. The case where the symbol is independent of the pole......Page all_21026_to_00269.cpc0167.djvu
§36. The case where the symbol is dependent on pole. Regularization and domains of constancy of the index......Page all_21026_to_00269.cpc0168.djvu
§37. Equivalent regularization. Index theorem......Page all_21026_to_00269.cpc0170.djvu
§38. Equations with an integral taken over a closed manifold......Page all_21026_to_00269.cpc0182.djvu
§39. Extension by means of the parameter......Page all_21026_to_00269.cpc0190.djvu
§40. Systems of singular integral equations......Page all_21026_to_00269.cpc0194.djvu
§41. Singular integral equations in classes of Lipschitz functions......Page all_21026_to_00269.cpc0200.djvu
§42. Leading derivatives of volume potential......Page all_21026_to_00269.cpc0209.djvu
§43. Problem of the oblique derivative......Page all_21026_to_00269.cpc0213.djvu
§44. Inequality involving the tangential and normal components of the gradient of a harmonic function......Page all_21026_to_00269.cpc0218.djvu
§45. Equilibrium of an isotropic elastic body......Page all_21026_to_00269.cpc0220.djvu
§46. Diffraction of stationary elastic waves......Page all_21026_to_00269.cpc0230.djvu
Appendix. Multipliers of Fourier Integrals......Page all_21026_to_00269.cpc0235.djvu
Bibliography......Page all_21026_to_00269.cpc0251.djvu
Index......Page all_21026_to_00269.cpc0261.djvu
Other Titles in the Series......Page all_21026_to_00269.cpc0267.djvu