Perturbation of Continuious Spectra And Singular Integral Operators
Perturbation of Continuious Spectra And Singular Integral Operators
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•s • ;■. F (w)0 . Lor. 7"'^] EUitt . (i- -15- CX3 J -00 |G(u)|^du = j |G^(u(i))|2di 2 2 If G(u) e L (-co, co), then P(v) e L (~co, c») . Furthermore, 00 CO j |P(v)|^dv = I lG(u)|^du . [5] . -00 -00 We now set P(v) = •^^^- v/TxC v) -a) (b-A( v) ) F, (v) . CO b lF(v)l^dv = ! lF^(v(X))|^dX . -00 a Then Furthermore, ^^^^^^) =tt^/3T'-'-"^ l-5^|^(logii|)(log^) T^TTK — 1 (2^)-^/^ 5--, 6>o _, ^, , (f) ^>:Fi7X-T?T^:i) G, (u(i))d^ = —/— T— 1 . I. M 1. 6 |^(lcgii|)(log|^) e 7i' 2 5->0, 6>0 ^^g /7IF)U-a)(b...-X) G^(u(^))di . Similarly, G-, (u(s)) = 4/^ l. I. M. { ^-5 i M^^ 1+^wi^^ \-ax r - o:;;(iog Y~^)(iog -r-rr) 2i^-^^fe iri b-' F^(v(\))d\ . ^■"^ x/a-^'^)(\-a)(b-X) Next, we turn to Lemma i|. L t The finite Hilbert transform Kx(X) = 1 P f ^ dix ■yq A-r"] ^ '■ vb"! (v) ■/■. ;!> ■i. I d+L- d-d mi'- A - * ! J. 3 (U)«) •> taioimari. +ti. '^ C. Sr ■■I'TfvI'cTjlP -16- 2 is a bounded operator on L (a, b) with norm l|K|f
What to read after Perturbation of Continuious Spectra And Singular Integral Operators?
You can find similar books in the "Read Also" column, or choose other free books by W Koppelman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
•s • ;■. F (w)0 . Lor. 7"'^] EUitt . (i- -15- CX3 J -00 |G(u)|^du = j |G^(u(i))|2di 2 2 If G(u) e L (-co, co), then P(v) e L (~co, c») . Furthermore, 00 CO j |P(v)|^dv = I lG(u)|^du . [5] . -00 -00 We now set P(v) = •^^^- v/TxC v) -a) (b-A( v) ) F, (v) . CO b lF(v)l^dv = ! lF^(v(X))|^dX . -00 a Then Furthermore, ^^^^^^) =tt^/3T'-'-"^ l-5^|^(logii|)(log^) T^TTK — 1 (2^)-^/^ 5--, 6>o _, ^, , (f) ^>:Fi7X-T?T^:i) G, (u(i))d^ = —/— T— 1 . I. M 1. 6 |^(lcgii|)(log|^) e 7i' 2 5->0, 6>0 ^^g /7IF)U-a)(b...-X) G^(u(^))di . Similarly, G-, (u(s)) = 4/^ l. I. M. { ^-5 i M^^ 1+^wi^^ \-ax r - o:;;(iog Y~^)(iog -r-rr) 2i^-^^fe iri b-' F^(v(\))d\ . ^■"^ x/a-^'^)(\-a)(b-X) Next, we turn to Lemma i|. L t The finite Hilbert transform Kx(X) = 1 P f ^ dix ■yq A-r"] ^ '■ vb"! (v) ■/■. ;!> ■i. I d+L- d-d mi'- A - * ! J. 3 (U)«) •> taioimari. +ti. '^ C. Sr ■■I'TfvI'cTjlP -16- 2 is a bounded operator on L (a, b) with norm l|K|f
What to read after Perturbation of Continuious Spectra And Singular Integral Operators?
You can find similar books in the "Read Also" column, or choose other free books by W Koppelman to read onlineMoreLess
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