Inverse Problems for Ultrahyperbolic Schr¨ odinger Equations Fikret G¨ olgeleyen and ¨ Ozlem Kaytmaz Department of Mathematics, Bulent Ecevit University, Zonguldak 67100 Turkey E-mail: f.golgeleyen@beun.edu.tr, ozlem.kaytmaz@beun.edu.tr Abstract. In this paper, we establish a global Carleman estimate for an Ultrahyper- bolic Schr¨ odinger equation. Moreover, we prove H¨ older stability for the inverse problem of determining a coefficient or a source term in the Ultrahyperbolic Schr¨ odinger equation by some lateral boundary data. Keywords. Ultrahyperbolic Schr¨ odinger equation, Inverse problem, Stability, Carle- man estimate ABSTRACT i∂$_{t}$v ( x, y, t ) + Δ$_{y}$ v ( x, y, t ) − Δ$_{x}$ v ( x, y, t ) − p ( x, y ) v ( x, y, t ) = 0 , ( x, y, t ) ∈ Q, (1.1) with the following initial and Dirichlet boundary data v ( x, y, 0) = a ( x, y ) , ( x, y ) ∈ D × G, (1.2) v ( x, y, t ) = 0 , ( x, y, t ) ∈ Σ . (1.3) 1 1. INTRODUCTION arXiv:1704.06780v1 [math.AP] 22 Apr 2017 Let n, m ∈ N , T > 0 and let D ⊂ R n be a bounded domain with smooth boundary ∂D and G = { y ∈ R $^{m}$; | y | < L } for L > 0 . We set Q = D × G × (0 , T ), Σ = ∂D × G × (0 , T ) and i = √ − 1 . We consider the ultrahyperbolic Schr¨ odinger equation