Gölgeleyen, Fikret; Yamamoto, Masahiro Uniqueness of solution of an inverse source problem for ultrahyperbolic equations. (English) Zbl 1446.45010 Inverse Probl. 36, No. 3, Article ID 035008, 17 p. (2020). MSC: 45K05 35L82 PDF BibTeX XML Cite \textit{F. Gölgeleyen} and \textit{M. Yamamoto}, Inverse Probl. 36, No. 3, Article ID 035008, 17 p. (2020; Zbl 1446.45010) Full Text: DOI
Gölgeleyen, Fikret; Kaytmaz, Özlem A Hölder stability estimate for inverse problems for the ultrahyperbolic Schrödinger equation. (English) Zbl 1428.35679 Anal. Math. Phys. 9, No. 4, 2171-2199 (2019). MSC: 35R30 35B35 35Q40 PDF BibTeX XML Cite \textit{F. Gölgeleyen} and \textit{Ö. Kaytmaz}, Anal. Math. Phys. 9, No. 4, 2171--2199 (2019; Zbl 1428.35679) Full Text: DOI
Lienert, Matthias; Petrat, Sören; Tumulka, Roderich Multi-time wave functions versus multiple timelike dimensions. (English) Zbl 1383.81091 Found. Phys. 47, No. 12, 1582-1590 (2017). MSC: 81Q35 53C50 81R20 PDF BibTeX XML Cite \textit{M. Lienert} et al., Found. Phys. 47, No. 12, 1582--1590 (2017; Zbl 1383.81091) Full Text: DOI
Lyakhov, Lev N.; Shishkina, Elina L. Weighted mixed spherical means and singular ultrahyperbolic equation. (English) Zbl 1338.42027 Analysis, München 36, No. 2, 65-70 (2016). MSC: 42B37 35L81 42B20 PDF BibTeX XML Cite \textit{L. N. Lyakhov} and \textit{E. L. Shishkina}, Analysis, München 36, No. 2, 65--70 (2016; Zbl 1338.42027) Full Text: DOI
Lyakhov, L. N.; Polovinkin, I. P.; Shishkina, E. L. Formulas for the solution of the Cauchy problem for a singular wave equation with Bessel time operator. (English. Russian original) Zbl 1325.35118 Dokl. Math. 90, No. 3, 737-742 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 459, No. 5, 533-538 (2014). MSC: 35L81 35C15 PDF BibTeX XML Cite \textit{L. N. Lyakhov} et al., Dokl. Math. 90, No. 3, 737--742 (2014; Zbl 1325.35118); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 459, No. 5, 533--538 (2014) Full Text: DOI
Gölgeleyen, Fikret; Yamamoto, Masahiro Stability of inverse problems for ultrahyperbolic equations. (English) Zbl 1335.35295 Chin. Ann. Math., Ser. B 35, No. 4, 527-556 (2014). Reviewer: Dan-Mircea Borş (Iaşi) MSC: 35R30 35A25 35B35 PDF BibTeX XML Cite \textit{F. Gölgeleyen} and \textit{M. Yamamoto}, Chin. Ann. Math., Ser. B 35, No. 4, 527--556 (2014; Zbl 1335.35295) Full Text: DOI
Pavšič, Matej Localized propagating tachyons in extended relativity theories. (English) Zbl 1292.35292 Adv. Appl. Clifford Algebr. 23, No. 2, 469-495 (2013). MSC: 35Q75 83D05 PDF BibTeX XML Cite \textit{M. Pavšič}, Adv. Appl. Clifford Algebr. 23, No. 2, 469--495 (2013; Zbl 1292.35292) Full Text: DOI
Kable, Anthony C. The Heisenberg ultrahyperbolic equation: \(K\)-finite and polynomial solutions. (English) Zbl 1287.22003 Kyoto J. Math. 52, No. 4, 839-894 (2012). Reviewer: Isolda E. Cardoso (Rosario) MSC: 22E30 22E25 22E47 35C11 35C15 35R03 PDF BibTeX XML Cite \textit{A. C. Kable}, Kyoto J. Math. 52, No. 4, 839--894 (2012; Zbl 1287.22003) Full Text: DOI Euclid
Udrişte, Constantin Riemann flow and Riemann wave. (English) Zbl 1224.53104 An. Univ. Vest Timiş., Ser. Mat.-Inform. 48, No. 1-2, 265-274 (2010). MSC: 53C44 58J35 58J45 PDF BibTeX XML Cite \textit{C. Udrişte}, An. Univ. Vest Timiş., Ser. Mat.-Inform. 48, No. 1--2, 265--274 (2010; Zbl 1224.53104)
Ren, Guang Bin; Kähler, Uwe Almansi decomposition for poly-ultrahyperbolic functions. (English) Zbl 1178.31003 Acta Math. Sin., Engl. Ser. 25, No. 9, 1561-1566 (2009). MSC: 31A30 35C10 PDF BibTeX XML Cite \textit{G. B. Ren} and \textit{U. Kähler}, Acta Math. Sin., Engl. Ser. 25, No. 9, 1561--1566 (2009; Zbl 1178.31003) Full Text: DOI
Craig, Walter; Weinstein, Steven On determinism and well-posedness in multiple time dimensions. (English) Zbl 1181.35140 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2110, 3023-3046 (2009). MSC: 35L15 35G10 35R25 PDF BibTeX XML Cite \textit{W. Craig} and \textit{S. Weinstein}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2110, 3023--3046 (2009; Zbl 1181.35140) Full Text: DOI arXiv
Kirichenko, E. V. On solution of equation, arising in the Dirichlet problem for ultrahyperbolic equation in a ball. (Russian) Zbl 1137.33316 Tr. Inst. Prikl. Mat. Mekh. 10, 59-71 (2005). Reviewer: Nikolai V. Krasnoschok (Donetsk) MSC: 33D90 34B08 PDF BibTeX XML Cite \textit{E. V. Kirichenko}, Tr. Inst. Prikl. Mat. Mekh. 10, 59--71 (2005; Zbl 1137.33316)
Kenig, C. E.; Ponce, G.; Rolvung, C.; Vega, L. Variable coefficient Schrödinger flows for ultrahyperbolic operators. (English) Zbl 1088.35065 Adv. Math. 196, No. 2, 373-486 (2005). Reviewer: Alberto Parmeggiani (Bologna) MSC: 35Q55 35S05 35B45 35L82 PDF BibTeX XML Cite \textit{C. E. Kenig} et al., Adv. Math. 196, No. 2, 373--486 (2005; Zbl 1088.35065) Full Text: DOI arXiv
Kobayashi, Toshiyuki; Ørsted, Bent Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\). (English) Zbl 1039.22005 Adv. Math. 180, No. 2, 551-595 (2003). Reviewer: A. A. Bogush (Minsk) MSC: 22E45 PDF BibTeX XML Cite \textit{T. Kobayashi} and \textit{B. Ørsted}, Adv. Math. 180, No. 2, 551--595 (2003; Zbl 1039.22005) Full Text: DOI arXiv
Ortner, Norbert; Wagner, Peter Deduction of L. Hörmander’s extension of Ásgeirsson’s mean value theorem. (English) Zbl 1054.35034 Bull. Sci. Math. 127, No. 10, 835-843 (2003). MSC: 35L82 35B05 35C05 PDF BibTeX XML Cite \textit{N. Ortner} and \textit{P. Wagner}, Bull. Sci. Math. 127, No. 10, 835--843 (2003; Zbl 1054.35034) Full Text: DOI
David, Liana The \(X\)-ray transform for currents. (English) Zbl 1040.32018 Differ. Geom. Appl. 18, No. 1, 113-117 (2003). Reviewer: Bernd Kreußler (Limerick) MSC: 32L25 53C65 53C15 53C28 PDF BibTeX XML Cite \textit{L. David}, Differ. Geom. Appl. 18, No. 1, 113--117 (2003; Zbl 1040.32018) Full Text: DOI
Sritanratana, G.; Kananthai, A. On the nonlinear Diamond operator related to the wave equation. (English) Zbl 1021.35074 Nonlinear Anal., Real World Appl. 3, No. 4, 465-470 (2002). MSC: 35M20 35L05 PDF BibTeX XML Cite \textit{G. Sritanratana} and \textit{A. Kananthai}, Nonlinear Anal., Real World Appl. 3, No. 4, 465--470 (2002; Zbl 1021.35074) Full Text: DOI
Amirov, A. Kh. On a class of inverse problems for an ultrahyperbolic equation. (English. Russian original) Zbl 1048.35126 Dokl. Math. 64, No. 1, 22-24 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 379, No. 2, 151-153 (2001). MSC: 35R30 35L82 PDF BibTeX XML Cite \textit{A. Kh. Amirov}, Dokl. Math. 64, No. 1, 151--153 (2001; Zbl 1048.35126); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 379, No. 2, 151--153 (2001)
Tong, Xiaojun; Dong, Dengke; Chen, Mianyun The mean value theorem and converse theorem of a class of higher order partial differential equations. (Chinese. English summary) Zbl 0966.35086 J. Math. Res. Expo. 20, No. 3, 401-405 (2000). MSC: 35M20 35Q05 35B05 PDF BibTeX XML Cite \textit{X. Tong} et al., J. Math. Res. Expo. 20, No. 3, 401--405 (2000; Zbl 0966.35086)
Kananthai, A. On the convolution equation related to the \(N\)-dimensional ultra-hyperbolic operator. (English) Zbl 0949.46014 J. Comput. Appl. Math. 115, No. 1-2, 301-308 (2000). Reviewer: P.Craciunas (Iaşi) MSC: 46F10 35E05 35D10 PDF BibTeX XML Cite \textit{A. Kananthai}, J. Comput. Appl. Math. 115, No. 1--2, 301--308 (2000; Zbl 0949.46014) Full Text: DOI
Nikolayev, Dmitry I.; Schaeben, Helmut Characteristics of the ultrahyperbolic differential equation governing pole density functions. (English) Zbl 0943.35105 Inverse Probl. 15, No. 6, 1603-1619 (1999). MSC: 35R30 44A15 86A22 92C55 PDF BibTeX XML Cite \textit{D. I. Nikolayev} and \textit{H. Schaeben}, Inverse Probl. 15, No. 6, 1603--1619 (1999; Zbl 0943.35105) Full Text: DOI
Kharibegashvili, S. S. Boundary value problems for a class of systems of second-order partial differential equations. (English. Russian original) Zbl 0952.35070 Differ. Equations 34, No. 1, 117-125 (1998); translation from Differ. Uravn. 34, No. 1, 114-122 (1998). Reviewer: Valentin Chernyatin (Szczecin) MSC: 35L55 35L20 35D05 PDF BibTeX XML Cite \textit{S. S. Kharibegashvili}, Differ. Equations 34, No. 1, 117--125 (1998; Zbl 0952.35070); translation from Differ. Uravn. 34, No. 1, 114--122 (1998)
Kharibegashvili, S. On some boundary value problems for an ultrahyperbolic equation. (English) Zbl 0914.35073 Georgian Math. J. 5, No. 4, 341-360 (1998). MSC: 35L20 35A05 PDF BibTeX XML Cite \textit{S. Kharibegashvili}, Georgian Math. J. 5, No. 4, 341--360 (1998; Zbl 0914.35073) Full Text: DOI EMIS EuDML
Altín, A.; Kaya, M. Some extensions of Brill’s theorem. (English) Zbl 0914.35037 Hacet. Bull. Nat. Sci. Eng., Ser. B 26, 57-66 (1997). MSC: 35G05 35A22 35K05 PDF BibTeX XML Cite \textit{A. Altín} and \textit{M. Kaya}, Hacet. Bull. Nat. Sci. Eng., Ser. B 26, 57--66 (1997; Zbl 0914.35037)
Anikonov, Yu. E.; Bubnov, B. A.; Erokhin, G. N. Inverse and ill-posed sources problems. (English) Zbl 0905.35095 Inverse and Ill-posed Problems Series. Utrecht: VSP. 239 p. (1997). Reviewer: Gabriel Dimitriu (Iaşi) MSC: 35R30 35-02 86A10 PDF BibTeX XML Cite \textit{Yu. E. Anikonov} et al., Inverse and ill-posed sources problems. Utrecht: VSP (1997; Zbl 0905.35095)
Altin, Abdullah; Kaya, Meryem The extension of Bateman theorem for an ultrahyperbolic equation. (English) Zbl 0852.35027 Bull. Calcutta Math. Soc. 87, No. 6, 581-588 (1995). MSC: 35C05 35L99 PDF BibTeX XML Cite \textit{A. Altin} and \textit{M. Kaya}, Bull. Calcutta Math. Soc. 87, No. 6, 581--588 (1995; Zbl 0852.35027)
John, Fritz The ultrahyperbolic differential equation with four independent variables. (English) Zbl 0823.35030 Gindikin, Simon (ed.) et al., 75 years of Radon transform. Proceedings of the conference held at the Erwin Schrödinger International Institute for Mathematical Physics in Vienna, Austria, August 31-September 4, 1992. Cambridge, MA: International Press. Conf. Proc. Lect. Notes Math. Phys. 4, 301-323 (1994). MSC: 35G05 44A12 01A75 35L99 PDF BibTeX XML Cite \textit{F. John}, in: 75 years of Radon transform. Proceedings of the conference held at the Erwin Schrödinger International Institute for Mathematical Physics in Vienna, Austria, August 31-September 4, 1992. Cambridge, MA: International Press. 301--323 (1994; Zbl 0823.35030)
Polovinkin, I. P. On the mean value theorem for the wave equation. (Russian) Zbl 0986.35009 Vragov, V. N. (ed.), Nonclassical equations of mathematical physics. Novosibirsk: Novosibirskij Gosudarstvennyj Universitet. 50-62 (1993). Reviewer: V.Grebenev (Novosibirsk) MSC: 35B05 35L05 35R30 PDF BibTeX XML Cite \textit{I. P. Polovinkin}, in: Neklassicheskie uravneniya matematicheskoj fiziki. Novosibirsk: Novosibirskij Gosudarstvennyj Universitet. 50--62 (1993; Zbl 0986.35009)
Woodhouse, N. M. J. Contour integrals for the ultrahyperbolic wave equation. (English) Zbl 0803.58053 Proc. R. Soc. Lond., Ser. A 438, No. 1902, 197-206 (1992). MSC: 58J45 35L05 PDF BibTeX XML Cite \textit{N. M. J. Woodhouse}, Proc. R. Soc. Lond., Ser. A 438, No. 1902, 197--206 (1992; Zbl 0803.58053) Full Text: DOI
Savëlova, T. I. A numerical algorithm for solving the Cauchy characteristic problem for ultrahyperbolic equations. (English. Russian original) Zbl 0721.65074 U.S.S.R. Comput. Math. Math. Phys. 30, No. 1, 233-237 (1990); translation from Zh. Vychisl. Mat. Mat. Fiz. 30, No. 2, 320-325 (1990). MSC: 65Z05 35L15 35Q60 78A10 PDF BibTeX XML Cite \textit{T. I. Savëlova}, U.S.S.R. Comput. Math. Math. Phys. 30, No. 1, 233--237 (1990; Zbl 0721.65074); translation from Zh. Vychisl. Mat. Mat. Fiz. 30, No. 2, 320--325 (1990) Full Text: DOI
Savëlova, T. I. A numerical algorithm for solving the characteristic Cauchy problem for ultrahyperbolic equations. (Russian) Zbl 0697.65092 Zh. Vychisl. Mat. Mat. Fiz. 30, No. 2, 320-325 (1990). Reviewer: G.Hedstrom MSC: 65Z05 35Q99 35L30 78A10 PDF BibTeX XML Cite \textit{T. I. Savëlova}, Zh. Vychisl. Mat. Mat. Fiz. 30, No. 2, 320--325 (1990; Zbl 0697.65092)
Barannik, L. F.; Lagno, V. I.; Fushchich, V. I. Subalgebras of the Poincaré algebra AP(2,3) and symmetry reduction of the nonlinear ultrahyperbolic d’Alembert equation. II. (English. Russian original) Zbl 0717.35061 Ukr. Math. J. 41, No. 5, 501-505 (1989); translation from Ukr. Mat. Zh. 41, No. 5, 579-584 (1989). Reviewer: V.Chernyatin MSC: 35L99 17B81 PDF BibTeX XML Cite \textit{L. F. Barannik} et al., Ukr. Math. J. 41, No. 5, 501--505 (1989; Zbl 0717.35061); translation from Ukr. Mat. Zh. 41, No. 5, 579--584 (1989) Full Text: DOI
Melin, Anders On the use of intertwining operators in inverse scattering. (English) Zbl 0702.35240 Schrödinger operators, Proc. Nord. Summer Sch. Math., Sandbjerg Slot, Sønderborg/Denmark 1988, Lect. Notes Phys. 345, 383-400 (1989). Reviewer: Anders Melin MSC: 35R30 35J10 35P25 PDF BibTeX XML
Altin, Abduhllah; Young, Eutiquio C. Kelvin principle for a class of singular equations. (English) Zbl 0685.35005 Int. J. Math. Math. Sci. 12, No. 2, 385-390 (1989). MSC: 35A30 35C99 35L99 PDF BibTeX XML Cite \textit{A. Altin} and \textit{E. C. Young}, Int. J. Math. Math. Sci. 12, No. 2, 385--390 (1989; Zbl 0685.35005) Full Text: DOI EuDML
Ling, Ling; Geng, Guang The continuation of generalized potential solution of ultrahyperbolic equations. (Chinese. English summary) Zbl 0693.35022 J. Northwest Univ., Nat. Sci. 18, No. 1, 44-54 (1988). MSC: 35B60 35L99 PDF BibTeX XML
Barannik, L. F.; Lagno, V. I.; Fushchich, V. I. Subalgebras of the Poincaré algebra AP(2,3) and the symmetric reduction of the nonlinear ultrahyperbolic d’Alembert equation. I. (English. Russian original) Zbl 0683.35056 Ukr. Math. J. 40, No. 4, 351-356 (1988); translation from Ukr. Mat. Zh. 40, No. 4, 411-416 (1988). Reviewer: J.Tian MSC: 35L99 PDF BibTeX XML Cite \textit{L. F. Barannik} et al., Ukr. Math. J. 40, No. 4, 351--356 (1988; Zbl 0683.35056); translation from Ukr. Mat. Zh. 40, No. 4, 411--416 (1988) Full Text: DOI
Lambert, D.; Ronveaux, A. Elliptic and ultrahyperbolic differential operators connected by Hurwitz transformations. (English) Zbl 0659.35003 Bull. Soc. Math. Belg., Sér. B 40, No. 1, 11-23 (1988). MSC: 35A30 35J05 35L05 PDF BibTeX XML Cite \textit{D. Lambert} and \textit{A. Ronveaux}, Bull. Soc. Math. Belg., Sér. B 40, No. 1, 11--23 (1988; Zbl 0659.35003)
Liu, Jiapei Extension of Huygens’ principle to the nonhomogeneous ultrahyperbolic equation. (Chinese. English summary) Zbl 0676.35048 Chin. Ann. Math., Ser. A 8, No. 1-5, 95-101 (1987). Reviewer: J.Tian MSC: 35L10 35B40 35A30 PDF BibTeX XML Cite \textit{J. Liu}, Chin. Ann. Math., Ser. A 8, No. 1--5, 95--101 (1987; Zbl 0676.35048)
Stetkaer, Henrik Representations of groups on eigenspaces of invariant differential operators. (English) Zbl 0653.47030 Partial differential equations, Banach Cent. Publ. 19, 301-309 (1987). Reviewer: M.Tsuji MSC: 47F05 58J70 47A15 47A67 PDF BibTeX XML
Melin, Anders Intertwining methods in the problem of inverse scattering. (English) Zbl 0618.35029 Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1986, Conf. No. 5, 8 p. (1986). Reviewer: S.Tajima MSC: 35J10 35P25 35R30 47A40 PDF BibTeX XML Full Text: Numdam EuDML
Finch, David V. Cone beam reconstruction with sources on a curve. (English) Zbl 0579.65136 SIAM J. Appl. Math. 45, 665-673 (1985). Reviewer: C.L.Koul MSC: 65R10 44A15 58J40 PDF BibTeX XML Cite \textit{D. V. Finch}, SIAM J. Appl. Math. 45, 665--673 (1985; Zbl 0579.65136) Full Text: DOI
Kokebaev, B. K. On the correct boundary value problems for some differential equations. (Russian) Zbl 0537.35018 Boundary value problems for differential equations and their applications in mechanics and technology, Collect. Artic., Alma-Ata 1983, 80-85 (1983). Reviewer: W.Okrasiński MSC: 35G15 35K70 35K20 35L20 PDF BibTeX XML
Sin Don Kha A problem of mixed type for a class of hyperbolic equations. (Russian) Zbl 0545.35050 Boundary value problems for nonlinear equations, Collect. sci. Works, Novosibirsk 1982, 84-92 (1982). Reviewer: K.Barckow MSC: 35L05 35A05 35B40 PDF BibTeX XML
Altin, Abdullah Some expansion formulas for a class of singular partial differential equations. (English) Zbl 0486.35018 Proc. Am. Math. Soc. 85, 42-46 (1982). MSC: 35C05 35G05 35C10 PDF BibTeX XML Cite \textit{A. Altin}, Proc. Am. Math. Soc. 85, 42--46 (1982; Zbl 0486.35018) Full Text: DOI
Domshlak, Yu. I.; Tamoev, G. I. A vector analogue of the Picone-Hartman-Winter comparison theorem for partial differential operator equations and its application. (Russian) Zbl 0475.35010 Izv. Akad. Nauk Az. SSR, Ser. Fiz.- Tekh. Mat. Nauk 1981, No. 3, 21-26 (1981). MSC: 35B05 35L99 PDF BibTeX XML Cite \textit{Yu. I. Domshlak} and \textit{G. I. Tamoev}, Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk 1981, No. 3, 21--26 (1981; Zbl 0475.35010)
Moses, H. E. A kernel of Gel’fand-Levitan type for the three-dimensional Schrödinger equation. (English) Zbl 0453.35071 J. Math. Phys. 21, 83-89 (1980). MSC: 35Q99 35J10 PDF BibTeX XML Cite \textit{H. E. Moses}, J. Math. Phys. 21, 83--89 (1980; Zbl 0453.35071) Full Text: DOI
Young, Eutiqio C. Uniqueness of solutions of the Neumann problem for singular ultrahyperbolic equations. (English) Zbl 0434.35063 Port. Math. 36, 97-102 (1977). MSC: 35L99 35A05 PDF BibTeX XML Cite \textit{E. C. Young}, Port. Math. 36, 97--102 (1977; Zbl 0434.35063) Full Text: EuDML