502

§5.2 �ݘm 5.2.1 �ݘm�Vg ½Â 5.2.1 � X ´˜‡D‰˜m, P X∗ = B(X, K), Ù¥, B(X, K) = {Xþ½Â��Nk.‚5¼}, ¡ X∗ ´ X ��ݘm. 1/3 §5.2 �ݘm 5.2.1 �ݘm�Vg ½Â 5.2.1 � X ´˜‡D‰˜m, P X∗ = B(X, K), Ù¥, B(X, K) = {Xþ½Â��Nk.‚5¼}, ¡ X∗ ´ X ��ݘm. 1/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5.2.2 Lp[a, b] ��ݘm ½n 5.2.2 f ´ Lp[a, b] þ�k.‚5¼, K3 ˜� y(t) ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, … ‖f‖ = ‖y‖q = (∫ b a |y(t)|qdt ) 1 q . ‡ƒ, éu ∀y ∈ Lq[a, b], þª½Â Lp[a, b] þ�˜‡ k.‚5¼. 2/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3 5 1 X = Lp[a, b], K X∗ = Lq[a, b]. = ∀f ∈ X∗, ∃y ∈ Lq[a, b], �� f(x) = ∫ b a x(t)y(t)dt, = f Ú y ˜˜éA. 3�åÓ�¿Âe, (Lp[a, b])∗ Ú Lq[a, b] ƒ�. 3/3