Paragraph Experiment

Terms: Paragraph Experiment (283),

Terms: researcher (131,000,000), researchers (362,000,000),

Terms: poles of the scattering matrix (714), the scattering matrix (57,300), scattering matrix (150,000), scattering matrices (29,500), resonance expansion (520),

Terms: waves on the real (189), waves on the real line (17), resonances near the real axis (161), resonances * the real (471), resonance * the real (1,240), scattering * the real (569), the real line (499,000), the real axis (322,000),

Theory and Computation of Resonances in 1D Scattering - Resonance expansion for waves on the real line

S.H. Tang and M. Zworski, Potential scattering on the real line - We call them plane waves. Clearly, there exists no solution of (1.1) with only incoming terms or only outgoing terms for frequency <> 0. However, for frequency = 0, the solution u=(A+B) is considered both incoming and outgoing.

v(t; x) = A*exp(i*lamba) + B *exp(i*-lambda) = A + B when lambda=0

Terms: resonant states (35,800), distribution of resonances (1,100), approximating resonances (25), long lived resonances (1,180),

Terms: a generic potential (566), wave expansions (5,560), peaks of the scattering cross sections (1), phase shift transitions (40),

Terms: lax-phillips (3,840), lax * phillips (5,480), lax and phillips (468), nagy-foias (859), generalized backscattering (23),

Terms: scattering poles (2,200), eigenvalues of systems (59), scattering operator (24,000), trapped rays (1,730), tensor fields (88,500), tensor tomography (1,850), eigenvalues (3,860,000), eigenfunctions (595,000), random matrices (321,000), anisotropic metrics (203),

Terms: molecular imaging (2,520,000),

Plamen D Stefanov: Interests -  publications - earlier publications

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Terms: this work (211,000,000), work deals (701,000), deals with (107,000,000), with scattering (81,000), scattering by (613,000), by obstacles (216,000), obstacles which (944,000), which are (688,000,000), are finite (1,560,000), finite disjoint (15,300), disjoint unions (27,900), unions of (2,620,000), of strictly (1,610,000), strictly convex (171,000), convex bodies (103,000), bodies with (5,720,000), with smooth (7,030,000), smooth boundaries (25,500), boundaries in (6,480,000), in an (1,490,000,000), an odd (35,600,000), odd dimensional (34,600), dimensional euclidean (235,000), euclidean space. (943,000), space. the (41,600,000), the class (169,000,000), class of (147,000,000), of obstacles (4,650,000), obstacles of (1,450,000), of this (3,790,000,000), this type (173,000,000), type is (28,500,000), is considered (170,000,000), considered which (635,000), which are (688,000,000), are contained (15,400,000), contained in (219,000,000), in a (5,520,000,000), a given (155,000,000), given large (335,000), large ball (798,000), ball and (55,100,000), and have (996,000,000), have some (430,000,000), some additional (26,400,000), additional properties (1,180,000), properties its (379,000), its connected (623,000), connected components (740,000), components have (3,450,000), have bounded (89,600), bounded eccentricity (127), eccentricity the (107,000), the distances (5,560,000), distances between (5,050,000), between different (27,300,000), different connected (27,000), connected components (740,000), components are (26,500,000), are bounded (1,140,000), bounded from (401,000), from below (18,300,000), below and (215,000,000), and a (3,580,000,000), a uniform (26,600,000), uniform no (358,000), no eclipse (250,000), eclipse condition (376), condition is (29,700,000), is satisfied. (14,200,000), satisfied. it (1,300,000), it is (4,620,000,000), is shown (106,000,000), shown that (98,900,000), that if (498,000,000), if an (121,000,000), an obstacle (13,000,000), obstacle k (418), k in (13,900,000), in this (3,800,000,000), this class (51,100,000), class has (11,200,000), has connected (1,370,000), connected components (740,000), components of (94,900,000), of sufficiently (733,000), sufficiently small (1,320,000), small diameters (157,000), diameters then (2,990), then there (40,100,000), there exists (19,500,000), exists a (13,800,000), a horizontal (14,300,000), horizontal strip (197,000), strip near (225,000), near the (323,000,000), the real (708,000,000), real axis (429,000), axis in (3,430,000), in the (6,910,000,000), the complex (70,000,000), complex upper (49,900), upper half-plane (110,000), half-plane containing (844), containing infinitely (2,180), infinitely many (1,450,000), many scattering (2,780), scattering resonances (13,300), resonances poles (213), poles of (2,820,000), of the (6,530,000,000), the scattering (2,220,000), scattering matrix (150,000), matrix i.e. (162,000), i.e. the (64,900,000), the modified (16,300,000), modified lax-phillips (20), lax-phillips conjecture (75), conjecture holds (46,700), holds for (11,800,000), for such (178,000,000), such k (46,100), k this (3,570,000), this generalizes (97,600), generalizes a (65,100), a well-known (48,000,000), well-known result (156,000), result of (518,000,000), of m. (46,000,000), m. ikawa (26,000), ikawa concerning (5), concerning balls (431), balls with (4,430,000), with the (5,550,000,000), the same (2,920,000,000), same sufficiently (696), sufficiently small (1,320,000), small radius (406,000),

Terms: this work deals (98,800), work deals with (566,000), deals with scattering (147), with scattering by (477), scattering by obstacles (752), by obstacles which (1,100), obstacles which are (50,000), which are finite (37,400), are finite disjoint (380), finite disjoint unions (870), disjoint unions of (11,700), unions of strictly (18), of strictly convex (2,080), strictly convex bodies (332), convex bodies with (1,980), bodies with smooth (1,110), with smooth boundaries (3,460), smooth boundaries in (499), boundaries in an (72,800), in an odd (2,680,000), an odd dimensional (3,430), odd dimensional euclidean (145), dimensional euclidean space. (168,000), euclidean space. the (41,700), space. the class (11,800), the class of (25,700,000), class of obstacles (347), of obstacles of (13,400), obstacles of this (13,200), of this type (31,200,000), this type is (2,230,000), type is considered (68,900), is considered which (46,600), considered which are (41,900), which are contained (1,180,000), are contained in (11,200,000), contained in a (13,600,000), in a given (26,400,000), a given large (13,300), given large ball (5), large ball and (28,900), ball and have (200,000), and have some (18,000,000), have some additional (744,000), some additional properties (31,600), additional properties its (43), properties its connected (6), its connected components (13,500), connected components have (794), components have bounded (25), have bounded eccentricity (8), bounded eccentricity the (8), eccentricity the distances (8), the distances between (1,180,000), distances between different (23,000), between different connected (140), different connected components (4,880), connected components are (22,100), components are bounded (442), are bounded from (21,800), bounded from below (112,000), from below and (1,050,000), below and a (3,650,000), and a uniform (530,000), a uniform no (12,200), uniform no eclipse (5), no eclipse condition (10), eclipse condition is (21), condition is satisfied. (537,000), is satisfied. it (96,600), satisfied. it is (258,000), it is shown (11,200,000), is shown that (4,130,000), shown that if (975,000), that if an (4,590,000), if an obstacle (39,700), an obstacle k (43), obstacle k in (15), k in this (222,000), in this class (11,300,000), this class has (1,080,000), class has connected (43), has connected components (267), connected components of (153,000), components of sufficiently (92), of sufficiently small (24,100), sufficiently small diameters (99), small diameters then (21), diameters then there (29), then there exists (1,270,000), there exists a (10,300,000), exists a horizontal (431), a horizontal strip (33,100), horizontal strip near (118), strip near the (102,000), near the real (80,000), the real axis (321,000), real axis in (12,700), axis in the (878,000), in the complex (5,580,000), the complex upper (4,090), complex upper half-plane (1,770), upper half-plane containing (22), half-plane containing infinitely (4), containing infinitely many (1,380), infinitely many scattering (15), many scattering resonances (10), scattering resonances poles (13), resonances poles of (62), poles of the (970,000), of the scattering (461,000), the scattering matrix (57,300), scattering matrix i.e. (75), matrix i.e. the (31,700), i.e. the modified (1,750), the modified lax-phillips (16), modified lax-phillips conjecture (17), lax-phillips conjecture holds (5), conjecture holds for (21,000), holds for such (8,890), for such k (1,230), such k this (29), k this generalizes (145), this generalizes a (11,500), generalizes a well-known (616), a well-known result (76,900), well-known result of (30,100), result of m. (40,600), of m. ikawa (13), m. ikawa concerning (5), ikawa concerning balls (5), concerning balls with (6), balls with the (437,000), with the same (168,000,000), the same sufficiently (597), same sufficiently small (14), sufficiently small radius. (900),

Terms: this work deals with (90,200), work deals with scattering (10), deals with scattering by (27), with scattering by obstacles (12), scattering by obstacles which (13), by obstacles which are (65), obstacles which are finite (12), which are finite disjoint (20), are finite disjoint unions (44), finite disjoint unions of (367), disjoint unions of strictly (12), unions of strictly convex (13), of strictly convex bodies (198), strictly convex bodies with (80), convex bodies with smooth (39), bodies with smooth boundaries (31), with smooth boundaries in (74), smooth boundaries in an (13), boundaries in an odd (13), in an odd dimensional (219), an odd dimensional euclidean (30), odd dimensional euclidean space. (71), dimensional euclidean space. the (9,340), euclidean space. the class (21), space. the class of (668), the class of obstacles (39), class of obstacles of (8), of obstacles of this (36), obstacles of this type (142), of this type is (1,100,000), this type is considered (17,000), type is considered which (14), is considered which are (139), considered which are contained (10), which are contained in (673,000), are contained in a (1,170,000), contained in a given (62,200), in a given large (564), a given large ball (5), given large ball and (5), large ball and have (17), ball and have some (1,920), and have some additional (14,300), have some additional properties (607), some additional properties its (3), additional properties its connected (4), properties its connected components (4), its connected components have (16), connected components have bounded (7), components have bounded eccentricity (5), have bounded eccentricity the (5), bounded eccentricity the distances (5), eccentricity the distances between (4), the distances between different (1,910), distances between different connected (4), between different connected components (23), different connected components are (53), connected components are bounded (17), components are bounded from (13), are bounded from below (5,530), bounded from below and (14,800), from below and a (15,400), below and a uniform (19), and a uniform no (35), a uniform no eclipse (4), uniform no eclipse condition (5), no eclipse condition is (5), eclipse condition is satisfied. (5), condition is satisfied. it (2,390), is satisfied. it is (37,200), satisfied. it is shown (180), it is shown that (3,840,000), is shown that if (76,000), shown that if an (10,500), that if an obstacle (264), if an obstacle k (4), an obstacle k in (7), obstacle k in this (4), k in this class (49), in this class has (43,200), this class has connected (6), class has connected components (4), has connected components of (14), connected components of sufficiently (4), components of sufficiently small (12), of sufficiently small diameters (14), sufficiently small diameters then (4), small diameters then there (4), diameters then there exists (4), then there exists a (774,000), there exists a horizontal (313), exists a horizontal strip (12), a horizontal strip near (63), horizontal strip near the (111), strip near the real (9), near the real axis (1,370), the real axis in (6,220), real axis in the (2,370), axis in the complex (1,460), in the complex upper (462), the complex upper half-plane (1,590), complex upper half-plane containing (4), upper half-plane containing infinitely (4), half-plane containing infinitely many (4), containing infinitely many scattering (4), infinitely many scattering resonances (9), many scattering resonances poles (5), scattering resonances poles of (13), resonances poles of the (40), poles of the scattering (1,150), of the scattering matrix (23,800), the scattering matrix i.e. (43), scattering matrix i.e. the (13), matrix i.e. the modified (4), i.e. the modified lax-phillips (5), the modified lax-phillips conjecture (16), modified lax-phillips conjecture holds (5), lax-phillips conjecture holds for (5), conjecture holds for such (30), holds for such k (10), for such k this (9), such k this generalizes (5), k this generalizes a (17), this generalizes a well-known (173), generalizes a well-known result (250), a well-known result of (17,900), well-known result of m. (29), result of m. ikawa (5), of m. ikawa concerning (5), m. ikawa concerning balls (5), ikawa concerning balls with (5), concerning balls with the (6), balls with the same (29,700), with the same sufficiently (13), the same sufficiently small (11), same sufficiently small radius. (4),